Regular versus singular order of contact on pseudoconvex hypersurfaces

The singular and regular type of a point on a real hypersurface $\mathcal H$ in $\mathbb C^n$ are shown to agree when the regular type is strictly less than 4. If $\mathcal H$ is pseudoconvex, we show they agree when the regular type is 4. A non-pseudoconvex example is given where the regular type is 4 and the singular type is infinite

Devonian Sandstone Lithostratigraphy, Northern Arkansas

Two areas of Devonian sandstone development may be recognized in northern Arkansas. In northwestern Arkansas, the Clifty Formation comprises a massively bedded, super mature quartz arenite of Middle Devonian age overlain by thinner bedded, phosphatic quartz arenite and chert breccia of the Sylamore Sandstone Member, Chattanooga Shale (Upper Devonian). This sequence overlies Ordovician strata (Powell or Everton) and is succeeded by the Chattanooga Shale and strata of Lower Mississippian age. In north-central Arkansas, the Clifty Formation is absent and the Chattanooga Shale may develop sandstone at its base and top. Occasionally the Chattanooga Shale is absent and the entire interval may be Upper Devonian sandstone. These Upper Devonian sandstones are phosphatic, mature quartz arenites referred to the Sylamore Member except where they overlie the Chattanooga Shale. In these cases, the sandstone is recognized as an informal upper member of the Chattanooga. Reports of Lower Mississippian Sylamore Sandstone in north-central Arkansas are regarded as misidentification of the Bachelor Formation (Middle Kinderhookian

The role of forecasts in monetary policy

Forecasts of future economic developments play an important role for the monetary policy decisions of central banks. For example, forecasts of goal variables can help central banks achieve their goals and make them more accountable to the public. There are two primary explanations for the benefits of forecasts. The first is that monetary policy affects goal variables such as inflation and output only with substantial lags. Policy actions should, therefore, be based on forecasts of goal variables at horizons consistent with policy lags and be taken when these forecasts are inconsistent with policy goals. Under such an approach, the quality of a central bank's forecasts and the effectiveness of its actions to bring forecasts into alignment with targets provide a basis for judging the performance of policymakers and for holding them accountable.> The second, and less intuitive, explanation is that by focusing on a forecast of only one variable -- inflation -- a central bank can potentially achieve multiple goals. This approach can be successful even if there are tradeoffs among the various goal variables. For example, the approach can combine a commitment to long-run price stability with concern for the effects of monetary policy on output.> Amato and Laubach argue that the lagged effects of monetary policy make the use of forecasts necessary. They also argue that delegating a single goal—such as inflation stabilization—to the central bank facilitates accountability, but at the risk of not achieving other goals. They then examine how the Eurosystem and the Bank of England, both of which have been assigned a single goal, address the existence of tradeoffs among goals. Finally, the authors provide evidence that a monetary policy aimed primarily at stabilizing inflation forecasts—as practiced by the Bank of England, for example—can, in fact, achieve multiple goals.Forecasting ; Monetary policy ; Banks and banking, Central

Supernova Resonance-Scattering Profiles in the Presence of External Illumination

We discuss a simple model for the formation of a supernova spectral line by resonance scattering in the presence of external illumination of the line-forming region by light from circumstellar interaction (toplighting). The simple model provides a clear understanding of the most conspicuous toplighting effect: a rescaling or, as we prefer, a ``muting'' of the line profile relative to the continuum. This effect would be present in more realistic models, but would be harder to isolate. An analytic expression for a muting factor for a P-Cygni line is derived that depends on the ratio E of the toplighting specific intensity to the specific intensity from the supernova photosphere. If E<1, the line profile is reduced in scale or ``muted''. If E=1, the line profile vanishes altogether. If E>1, the line profile flips vertically: then having an absorption component near the observer-frame line center wavelength and a blueshifted emission component.Comment: accepted for publication in PAS

Impact of the U.S. House of Representatives BTU Tax Proposal on Whole Farm and Enterprise Production Costs in Kansas

Agricultural and Food Policy, Agricultural Finance,