Estimating Percent Residue Cover Using the Line-Transect Method

Leaving crop residue on the soil surface is one of the easiest and most cost-effective methods of reducing soil erosion. Research in Nebraska and other midwestern states has shown that leaving as little as 20 percent of the soil surface covered with crop residue can reduce soil erosion by one-half of what it would be from residue-free conditions. Greater amounts of residue cover will further reduce erosion. Many Conservation Plans specify crop residue management or residue left on the soil surface as the primary erosion control method. Generally, the amount of cover required after planting ranges from 30 percent to as much as 85 percent. Thus, it is important to accurately determine percent residue cover to verify effective erosion control and compliance with a Conservation Plan. Residue cover cannot be estimated merely by looking across a field. Such estimates, often attempted from the road or edge of the field, grossly overestimate the actual amount of cover. Accurate estimates of residue cover can only be obtained from measurements taken within the field, while looking straight down at the soil and residue. Crop residue management, or leaving residue on the soil surface, is the most cost-effective method of reducing soil erosion available to Nebraska farmers. Accurate measurements of percent residue cover are needed to determine if enough cover is present to adequately reduce erosion and to comply with a Conservation Plan. The line-transect method is one of the easiest and most accurate methods of determining percent residue cover

Soft lithography molding of polymer integrated optical devices: Reduction of the background residue

Soft lithography molding is a promising technique for patterning polymer integrated optical devices, however the presence of a background residue has the potential to limit the usefulness of this technique. We present the soft lithography technique for fabricating polymer waveguides. Several effects of the background residue are investigated numerically, including the modal properties of an individual waveguide, the coupling ratio of a directional coupler, and the radiation loss in a waveguide bend. Experimentally, the residue is found to be reduced through dilution of the core polymer solution. We find that the force with which the soft mold is depressed on the substrate does not appreciably affect the waveguide thickness or the residue thickness. Optical microscope images show that the residue is thinnest next to the waveguide

Products in Residue Classes

We consider a problem of P. Erdos, A. M. Odlyzko and A. Sarkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results ``on average'' over moduli m and residue classes modulo m and somewhat stronger results when the average is restricted to prime moduli m = p. We also consider the analogous question wherein the primes are replaced by easier sequences so, quite naturally, we obtain much stronger results.Comment: 18 page

Decomposition of residue currents

Given a submodule $J\subset \mathcal O_0^{\oplus r}$ and a free resolution of $J$ one can define a certain vector valued residue current whose annihilator is $J$. We make a decomposition of the current with respect to Ass$(J)$ that correspond to a primary decomposition of $J$. As a tool we introduce a class of currents that includes usual residue and principal value currents; in particular these currents admit a certain type of restriction to analytic varieties and more generally to constructible sets