Extending the range of error estimates for radial approximation in Euclidean space and on spheres

We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of R^d and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.Comment: 10 page

Radiation Front Sweeping the Ambient Medium of Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are emitted by relativistic ejecta from powerful cosmic explosions. Their light curves suggest that the gamma-ray emission occurs at early stages of the ejecta expansion, well before it decelerates in the ambient medium. If so, the launched gamma-ray front must overtake the ejecta and sweep the ambient medium outward. As a result a gap is opened between the ejecta and the medium that surfs the radiation front ahead. Effectively, the ejecta moves in a cavity until it reaches a radius R_{gap}=10^{16}E_{54}^{1/2} cm where E is the isotropic energy of the GRB. At R=R_{gap} the gap is closed, a blast wave forms and collects the medium swept by radiation. Further development of the blast wave is strongly affected by the leading radiation front: the front plays the role of a precursor where the medium is loaded with e+- pairs and preaccelerated just ahead of the blast. It impacts the emission from the blast at R < R_{load}=5R_{gap} (the early afterglow). A spectacular observational effect results: GRB afterglows should start in optical/UV and evolve fast (< min) to a normal X-ray afterglow. The early optical emission observed in GRB 990123 may be explained in this way. The impact of the front is especially strong if the ambient medium is a wind from a massive progenitor of the GRB. In this case three phenomena are predicted: (1) The ejecta decelerates at R<R_{load} producing a lot of soft radiation. (2) The light curve of soft emission peaks at t_{peak}=40(1+z)E_{54}^{1/2}(Gamma_{ej}/100)^{-2} s where Gamma_{ej} is the Lorentz factor of the ejecta. Given measured redshift z and t_{peak}, one finds Gamma_{ej}. (3) The GRB acquires a spectral break at 5 - 50 MeV because harder photons are absorbed by radiation scattered in the wind.Comment: 20 pages, accepted to Ap

ON THE GEOMETRY OF THE X-RAY EMITTING REGION IN SEYFERT GALAXIES

For the first time, detailed radiative transfer calculations of Comptonized X-ray and gamma-ray radiation in a hot pair plasma above a cold accretion disk are performed using two independent codes and methods. The simulations include both energy and pair balance as well as reprocessing of the X- and gamma-rays by the cold disk. We study both plane-parallel coronae as well as active dissipation regions having shapes of hemispheres and pill boxes located on the disk surface. It is shown, contrary to earlier claims, that plane-parallel coronae in pair balance have difficulties in selfconsistently reproducing the ranges of 2-20 keV spectral slopes, high energy cutoffs, and compactnesses inferred from observations of type 1 Seyfert galaxies. Instead, the observations are consistent with the X-rays coming from a number of individual active regions located on the surface of the disk. A number of effects such as anisotropic Compton scattering, the reflection hump, feedback to the soft photon source by reprocessing, and an active region in pair equilibrium all conspire to produce the observed ranges of X-ray slopes, high energy cutoffs, and compactnesses. The spread in spectral X-ray slopes can be due to a spread in the properties of the active regions such as their compactnesses and their elevations above the disk surface. Simplified models invoking isotropic Comptonization in spherical clouds are no longer sufficient when interpreting the data.Comment: 9 pages, 3 postscript figures, figures can be obtained from the authors via e-mail: [email protected]

InAs/GaSb vertical nanowire TFETs on Si for digital and analogue applications

Vertical InAs/GaSb nanowire TFETs with diameters of 20 nm and 25 nm have been fabricated and characterized. The influence of diameter, gate-placement, and nanowire numbers have been studied. The best device shows a subthreshold swing of 68 mV/dec at VDS = 0.3 V and 26 μA/μm at VDS = 0.3 V and VGS = 0.5 V. It achieves a self-gain larger than 100 with high transconductance efficiency

Vertical InAs/GaAsSb/GaSb tunneling field-effect transistor on Si with S = 48 mV/decade and Ion = 10 μA/μm for Ioff = 1 nA/μm at VDS = 0.3 V

We present a vertical nanowire InAs/GaAsSb/GaSb TFET with a highly scaled InAs diameter (20 nm). The device exhibits a minimum subthreshold swing of 48 mV/dec. for Vds = 0.1-0.5 V and achieves an Ion = 10.6 μA/μm for Ioff = 1 nA/μm at Vds = 0.3 V. The lowest subthreshold swing achieved is 44 mV/dec. at Vds= 0.05 V. Furthermore, a benchmarking is performed against state-of-the-art TFETs and MOSFETs demonstrating a record high I60 and performance benefits for Vds between 0.1 and 0.3 V

Influence of corruption on economic growth rate and foreign investments

In order to investigate whether government regulations against corruption can affect the economic growth of a country, we analyze the dependence between Gross Domestic Product (GDP) per capita growth rates and changes in the Corruption Perceptions Index (CPI). For the period 1999-2004 on average for all countries in the world, we find that an increase of CPI by one unit leads to an increase of the annual GDP per capita by 1.7 %. By regressing only European transition countries, we find that $\Delta$CPI = 1 generates increase of the annual GDP per capita by 2.4 %. We also analyze the relation between foreign direct investments received by different countries and CPI, and we find a statistically significant power-law functional dependence between foreign direct investment per capita and the country corruption level measured by the CPI. We introduce a new measure to quantify the relative corruption between countries based on their respective wealth as measured by GDP per capita.Comment: 8 pages, 3 figures, elsart styl

X-ray Variability Characteristics of the Seyfert 1 Galaxy NGC 3783

We have characterized the energy-dependent X-ray variability properties of the Seyfert~1 galaxy NGC 3783 using archival XMM-Newton and Rossi X-ray Timing Explorer data. The high-frequency fluctuation power spectral density function (PSD) slope is consistent with flattening towards higher energies. Light curve cross correlation functions yield no significant lags, but peak coefficients generally decrease as energy separation of the bands increases on both short and long timescales. We have measured the coherence between various X-ray bands over the temporal frequency range of 6e-8 to 1e-4 Hz; this range includes the temporal frequency of the low-frequency power spectral density function (PSD) break tentatively detected by Markowitz et al. and includes the lowest temporal frequency over which coherence has been measured in any AGN to date. Coherence is generally near unity at these temporal frequencies, though it decreases slightly as energy separation of the bands increases. Temporal frequency-dependent phase lags are detected on short time scales; phase lags are consistent with increasing as energy separation increases or as temporal frequency decreases. All of these results are similar to those obtained previously for several Seyfert galaxies and stellar-mass black hole systems. Qualitatively, these results are consistent with the variability models of Kotov et al. and Lyubarskii, wherein the X-ray variability is due to inwardly propagating variations in the local mass accretion rate.Comment: Accepted for publication in The Astrophysical Journal, 2005, vol. 635, p. 180; version 2 has minor grammatical changes; 23 pages; uses emulateapj

Money in monetary policy design: monetary cross-checking in the New-Keynesian model

In the New-Keynesian model, optimal interest rate policy under uncertainty is formulated without reference to monetary aggregates as long as certain standard assumptions on the distributions of unobservables are satisfied. The model has been criticized for failing to explain common trends in money growth and inflation, and that therefore money should be used as a cross-check in policy formulation (see Lucas (2007)). We show that the New-Keynesian model can explain such trends if one allows for the possibility of persistent central bank misperceptions. Such misperceptions motivate the search for policies that include additional robustness checks. In earlier work, we proposed an interest rate rule that is near-optimal in normal times but includes a cross-check with monetary information. In case of unusual monetary trends, interest rates are adjusted. In this paper, we show in detail how to derive the appropriate magnitude of the interest rate adjustment following a significant cross-check with monetary information, when the New-Keynesian model is the central bank’s preferred model. The cross-check is shown to be effective in offsetting persistent deviations of inflation due to central bank misperceptions. Keywords: Monetary Policy, New-Keynesian Model, Money, Quantity Theory, European Central Bank, Policy Under Uncertaint