Sylvester's question and the Random Acceleration Process

Let n points be chosen randomly and independently in the unit disk. "Sylvester's question" concerns the probability p_n that they are the vertices of a convex n-sided polygon. Here we establish the link with another problem. We show that for large n this polygon, when suitably parametrized by a function r(phi) of the polar angle phi, satisfies the equation of the random acceleration process (RAP), d^2 r/d phi^2 = f(phi), where f is Gaussian noise. On the basis of this relation we derive the asymptotic expansion log p_n = -2n log n + n log(2 pi^2 e^2) - c_0 n^{1/5} + ..., of which the first two terms agree with a rigorous result due to Barany. The nonanalyticity in n of the third term is a new result. The value 1/5 of the exponent follows from recent work on the RAP due to Gyorgyi et al. [Phys. Rev. E 75, 021123 (2007)]. We show that the n-sided polygon is effectively contained in an annulus of width \sim n^{-4/5} along the edge of the disk. The distance delta_n of closest approach to the edge is exponentially distributed with average 1/(2n).Comment: 29 pages, 4 figures; references added and minor change

The politics of linking educational research, policy, and practice: The case of improving educational quality in Ghana, Guatemala and Mali

This paper examines the political dimension of the educational research undertaken by Ghanian,\ud Guatemalan, and Malian teams as part of the 1991 to 1996, USAID-funded “Improving Educational\ud Quality” (IEQ) project. The following questions are addressed: (a) why were (or were not) aspects\ud of the educational reforms studied by the researchers; (b) why were (or were not) research findings\ud used in decision-makingabout the educationalpolicies and practices associatedwith the reforms; and\ud (c) why were particular institutional arrangements and funding levels constituted for the research and\ud dialogue activity. In offering answers to these questions, attentionis paid to local, national, and global\ud power relations and resource distributions

A Single Circumbinary Disk in the HD 98800 Quadruple System

We present sub-arcsecond thermal infrared imaging of HD 98800, a young quadruple system composed of a pair of low-mass spectroscopic binaries separated by 0.8'' (38 AU), each with a K-dwarf primary. Images at wavelengths ranging from 5 to 24.5 microns show unequivocally that the optically fainter binary, HD 98800B, is the sole source of a comparatively large infrared excess upon which a silicate emission feature is superposed. The excess is detected only at wavelengths of 7.9 microns and longer, peaks at 25 microns, and has a best-fit black-body temperature of 150 K, indicating that most of the dust lies at distances greater than the orbital separation of the spectroscopic binary. We estimate the radial extent of the dust with a disk model that approximates radiation from the spectroscopic binary as a single source of equivalent luminosity. Given the data, the most-likely values of disk properties in the ranges considered are R_in = 5.0 +/- 2.5 AU, DeltaR = 13+/-8 AU, lambda_0 = 2(+4/-1.5) microns, gamma = 0+/-2.5, and sigma_total = 16+/-3 AU^2, where R_in is the inner radius, DeltaR is the radial extent of the disk, lambda_0 is the effective grain size, gamma is the radial power-law exponent of the optical depth, tau, and sigma_total is the total cross-section of the grains. The range of implied disk masses is 0.001--0.1 times that of the moon. These results show that, for a wide range of possible disk properties, a circumbinary disk is far more likely than a narrow ring.Comment: 11 page Latex manuscript with 3 postscript figures. Accepted for publication in Astrophysical Journal Letters. Postscript version of complete paper also available at http://www.hep.upenn.edu/PORG/web/papers/koerner00a.p

Full-wave invisibility of active devices at all frequencies

There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or "cloaking") from observation by electromagnetic (EM) waves. Here, we prove invisibility, with respect to solutions of the Helmholtz and Maxwell's equations, for several constructions of cloaking devices. Previous results have either been on the level of ray tracing [Le,PSS] or at zero frequency [GLU2,GLU3], but recent numerical [CPSSP] and experimental [SMJCPSS] work has provided evidence for invisibility at frequency $k\ne 0$. We give two basic constructions for cloaking a region $D$ contained in a domain $\Omega$ from measurements of Cauchy data of waves at \p \Omega; we pay particular attention to cloaking not just a passive object, but an active device within $D$, interpreted as a collection of sources and sinks or an internal current.Comment: Final revision; to appear in Commun. in Math. Physic

Identification of nonlinearity in conductivity equation via Dirichlet-to-Neumann map

We prove that the linear term and quadratic nonlinear term entering a nonlinear elliptic equation of divergence type can be uniquely identified by the Dirichlet to Neuman map. The unique identifiability is proved using the complex geometrical optics solutions and singular solutions

1400 Liter 1.8K Test Facility

A double bath superfluid helium dewar has been constructed and operated at Fermilab`s Magnet Test Facility. The 1.8 K portion of the dewar is sized to contain a superconducting magnet up to 0.5 meters in diameter and 4 meters long in a vertical orientation in 0.12 MPa pressurized superfluid. The dewar can also provide a subcooled Helium I environment for tests; the entire temperature range from 4.4 K to 1. 8 K at 0.12 MPa is available. This paper describes the system design, lambda plate, heat exchanger, and performance

Spitzer/IRS spectroscopy of high mass precursors to planetary nebulae

We present Spitzer/IRS observations of a small sample of heavily obscured IRAS sources displaying both the infrared and OH maser emission characteristic of OH/IR stars on the asymptotic giant branch (AGB), but also radio continuum emission typical of ionized planetary nebulae (PNe), the so-called OHPNe. Our observations show that their mid-infrared spectra are dominated by the simultaneous presence of strong and broad amorphous silicate absorption features together with crystalline silicate features, originated in their O-rich circumstellar shells. Out of the five sources observed, three of them are clearly non-variable at infrared wavelengths, confirming their post-AGB status, while the remaining two still show strong photometric fluctuations, and may still have not yet departed from the AGB. One of the non-variable sources in the sample, IRAS 17393-2727, displays a strong [Ne II] nebular emission at 12.8 microns, indicating that the ionization of its central region has already started. This suggests a rapid evolution from the AGB to the PN stage. We propose that these heavily obscured OHPNe represent the population of high mass precursors to PNe in our Galaxy.Comment: To appear in The Astrophysical Journal Letters (scheduled in the 2007 September 1 issue