Computing Bits of Algebraic Numbers

We initiate the complexity theoretic study of the problem of computing the bits of (real) algebraic numbers. This extends the work of Yap on computing the bits of transcendental numbers like \pi, in Logspace. Our main result is that computing a bit of a fixed real algebraic number is in C=NC1\subseteq Logspace when the bit position has a verbose (unary) representation and in the counting hierarchy when it has a succinct (binary) representation. Our tools are drawn from elementary analysis and numerical analysis, and include the Newton-Raphson method. The proof of our main result is entirely elementary, preferring to use the elementary Liouville's theorem over the much deeper Roth's theorem for algebraic numbers. We leave the possibility of proving non-trivial lower bounds for the problem of computing the bits of an algebraic number given the bit position in binary, as our main open question. In this direction we show very limited progress by proving a lower bound for rationals

Effect of Tillage Systems on the Variability of Soil-Water Tensions and Soil-Water Content

Field experiments were conducted on a Webster silty clay loam soil to study the effect of four different tillage systems (no-till, chisel plow, paraplow and moldboard plow) on soil-water tension and soil-water content. Data on soil-water tensions were collected by using tensiometers installed at 0.15, 0.3, 0.6, 0.9 and 1.5 m depths within the crop row. A portable pressure transducer equipped with a syringe needle and a digital pressure indicator was used to indicate soil-water tensions. Field data on soil-water tensions and volumetric soil-water contents for various tillage systems were collected during the 1983 and 1984 growing season. The results of this study indicated that tillage systems affected the soil-water tensions in the surface layer (0 to 0.3 m) of the soil in 1984, but the differences were not statistically significant at the 5% level in 1983. Results showed that the variability (standard deviation and range) of soil-water tensions increased when the soil became drier under all tillage systems, but the variability began to decrease at about 45 kPa of soil-water tension and continued to decrease further at higher values of soil-water tensions (reaching up to 80 kPa)

Stress-Day Factor and Stress-Day Index as Indicators of Drainage Needs of Soils

Field data on water-table depths, plant parameters, and corn yields were collected for 3 years (1984 through 1986) on the Clarion-Nicollet-Webster Soil Association from 50 plots under naturally fluctuating water-table conditions. The stress-day factor (SEW30) and stress-day index (SDI) concepts were used to provide a quantitative means of determining drainage needs of soils. Corn yield and SDI were used to assess the crop production losses due to excessive wetness in the soils. The stress-day factor and index were found to be useful tools in evaluation of drainage needs of poorly drained soils. The highest values of SEW30 and SDI were obtained for naturally very poorly drained soils, while naturally well-drained soils gave about zero values of SDI. Significant differences were found in SEW30 and SDI between all natural drainage classes of soils. This study also showed a strong relationship between relative yield and SDI for corn. This relationship was compared with published data from three other sources -India, North Carolina, and Ohio and found to be in agreement. The information in this paper on transient waterlogging\u27s effect on crop growth under different natural soil drainage regimes should provide a basis for improving the design of field drainage systems

Impact of Tillage, Crop Rotation, and Chemical Management Practices on Groundwater Quality

Contamination of groundwater by nitrate and pesticides has been documented by various state and federal agencies in the United States. Groundwater pollution is of increasing concern in the United States because about 50 percent of the drinking water comes from groundwater. A recent study suggested that water pollution is the most damaging and widespread environmental effect of agricultural production. Recent research conducted in Iowa and surrounding states has indicated the incidence of groundwater contamination by pesticides and nitrogen fertilizers (Baker and Johnson, 1981; Everts and Kanwar, 1990; Gast et al., 1978; Hallet al., 1989; Hallberg, 1989; Kanwar et al., 1985a, 1986, 1988, 1991). Elevated nitrate levels in groundwater because of agricultural activities also have been documented (Kanwar and Baker, 1991)

Hydrologic simulation of nitrate losses with tile drainage water

The processes of water movement and leaching of nitrates within the soil profile are complex, but important to agricultural production and the environment. The effects of our modern agricultural production technology on nitrate movement within and from watersheds need to be determined. The objective of this study was to develop mathematical models to describe the movement of nitrates in the soil profile and to predict the nitrate losses with tile drainage water;A mathematical model was developed to describe the movements of nitrates in a soil profile based on a zero-order reaction rate of nitrate reduction. This model is capable of predicting the concentration of nitrates at any time within the soil profile from a single time application of fertilizers on the soil surface. A second mathematical model was developed based on a first-order reaction rate of nitrate reduction. The validity of these models has been supported by comparison with experimental data;Also, a computer simulation model of nitrogen transformations and transport in soil was developed to predict nitrate concentrations in tile effluent as a function of farm management practices and climatic conditions. This model is based on a previously developed model and uses daily pan evaporation, and daily precipitation records as inputs. Other inputs to the model include planting and harvest dates, dates of fertilization, and initial moisture content nitrate concentrations in the soil profile. The various outputs from the model are tile flow, nitrate concentration in the effluent, evapotranspiration, and nitrogen uptake by plants;Predicted values of tile flow and concentration of nitrates in the tile effluent compared favorably with the values measured for the years from 1970 to 1978 at Agronomy and Agricultural Engineering Research Center in Boone County, Iowa. A sensitivity analysis of the model parameters related to tile drainage and nitrate concentrations in the tile water was completed. Water content in the unsaturated region and initial nitrate concentrations in the soil profile are the two important factors influencing the effluent concentrations

Crop Susceptibility Factors for Corn and Their Effect on Stress-Day Index

Field data on crop susceptibility factors (CS) and stress-day factors (SEW30) were reviewed and evaluated. The effects of CS factors and their corresponding values of normalized crop susceptibility factors (NCS) on the relationship between stress day index (SDI) and relative yield (RY) were evaluated. Different sets of CS and NCS values for corn, obtained from different locations in the world, were also compared. The results of this study indicate that the relationships developed between SDI and RY by using CS factors will be significantly different from the ones developed by using the corresponding NCS factors. Also, the use of CS values from other locations could be acceptable for calculating the SDI values for drainage design if local data on SEW30 factors are available

Testing Uniformity of Stationary Distribution

A random walk on a directed graph gives a Markov chain on the vertices of the graph. An important question that arises often in the context of Markov chain is whether the uniform distribution on the vertices of the graph is a stationary distribution of the Markov chain. Stationary distribution of a Markov chain is a global property of the graph. In this paper, we prove that for a regular directed graph whether the uniform distribution on the vertices of the graph is a stationary distribution, depends on a local property of the graph, namely if (u,v) is an directed edge then outdegree(u) is equal to indegree(v). This result also has an application to the problem of testing whether a given distribution is uniform or "far" from being uniform. This is a well studied problem in property testing and statistics. If the distribution is the stationary distribution of the lazy random walk on a directed graph and the graph is given as an input, then how many bits of the input graph do one need to query in order to decide whether the distribution is uniform or "far" from it? This is a problem of graph property testing and we consider this problem in the orientation model (introduced by Halevy et al.). We reduce this problem to test (in the orientation model) whether a directed graph is Eulerian. And using result of Fischer et al. on query complexity of testing (in the orientation model) whether a graph is Eulerian, we obtain bounds on the query complexity for testing whether the stationary distribution is uniform

Evaluation of Subsurface Drain Installation Methods Using Water Table and Drain Outflow Data

The performances of subsurface drains installed by two different methods (trench and trenchless) were compared using water table depths for two different periods (1980 through 1984 and 1990 through 1991). Data were gathered from a long-term study conducted at Iowa State University’s Northeast Research Center at Nashua, Iowa. Drain installation methods were also evaluated by using the drain outflow data for 1990 and 1991