Analogue of Ramanujan's function k(τ)k(\tau) for the continued fraction of order six

The Ramanujan's $k(\tau)$ function is defined as $k(\tau)=r(\tau)r(2\tau)^2$, where $r(\tau)$ is the Rogers-Ramanujan continued fraction. Inspired by the recent work of Park (2023) about the analogue of function $k(\tau)$ for the Ramanujan cubic continued fraction, we study certain modular and arithmetic properties of the function $w(\tau) = X(\tau)X(3\tau)$, where $X(\tau)$ is the continued fraction of order six introduced by Vasuki, Bhaskar and Sharath (2010). We consider $w(\tau)$ to be an analogue of $k(\tau)$ for the continued fraction $X(\tau)$

Nutrient Cycling in Forage Production Systems

In most forage production systems, the nutrients needed for plant growth are provided by microbially mediated breakdown and release of plant-available mineral nutrients from dead plant tissues, livestock excreta, soil organic matter, and geochemically bound mineral forms. Even in fertilized forage systems, determining appropriate fertilizer application rates requires a systems approach on the part of the manager (e.g., Di and Cameron, 2000; Rotz et al., 2002). Fertilizer additions are simply one input in the system of inputs, outputs, pools, and fluxes that characterize nutrient cycling in a particular ecosystem

Nitrogen and tillage management for corn following alfalfa

Rotating alfalfa with corn can increase corn yield potential through improved soil physical properties that enhance water infiltration and root extension, a reduction in disease and pest pressure (i.e., corn rootworm), and an enhanced soil microbial community

Denitrification under Pastures on Permeable Soils Helps Protect Ground Water Quality

Pastures have been implicated in ground water contamination by nitrate, especially in humid regions with thin or sandy soils (Stout et al., 2000). Significant losses can occur even under low N input, because available N from excreta patches often exceeds plant uptake capacity. Lack of evidence that appreciable nitrate leaching was occurring in established Midwestern USA pastures led us to test the hypothesis that denitrification was preventing or remediating nitrate loading. Higher denitrification rates have been found in the relatively limited number of trials since Ball & Ryden (1984) first reported the significance of this process in pastures

Soil moisture and temperature relationships under fallow in eastern Oregon

Time of stand establishment is a critical factor affecting yields of winter wheat and barley in the fallow-crop rotation areas of the Pacific Northwest. Farmers in this winter-rainfall region are dependent on residual moisture in the seed zone for germination, because significant precipitation does not usually occur until after the optimum planting dates. Moisture is maintained near the soil surface through the summer of the fallow period by the use of a soil or stubble mulch. The rate of moisture loss is relatively low during the summer, but seems to accelerate in late August and September. This loss dries the seed zone and forces either deeper planting to reach adequate moisture or delayed seeding until precipitation re-wets the seed zone. Both practices can result in late, less vigorous stands which have lower yield potential and provide less protection from erosion. The objectives of this study were to: 1) quantify changes in seed zone water content prior to seeding; 2) determine the cause of the accelerated loss; 3) substantiate the effect of planting date on the yield of one variety of winter wheat and one variety of winter barley; 4) investigate the effect of soil temperature on the rate of first and 70% emergence of these species in the field; and 5) develop a means of predicting the average last date of planting after which stand establishment is excessively delayed at one location in eastern Oregon. Although both years were abnormally wet in late summer and fall, significant losses of seed zone water content occurred in 1976. At 6 cm, the loss period occurred in early September; at 9, 12, 15, and 18 cm, the losses occurred in late September. The measured losses were not as great as expected. No significant losses were observed in 1977 because of frequent precipitation. My hypothesis was that increasing nighttime vapor pressure gradients from the moist seed zone to the soil surface develop because of the combination of warm days and cool, clear nights characteristic of late August and September in this area. Larger vapor pressure gradients would cause increased water losses from the profile. However, no correlation was found with calculated vapor pressure gradients, the occurrence of low surface temperatures at night, or average temperature gradients in the upper soil profile. Computer simulation of isothermal liquid flow was used to discern the relative contributions of evaporative losses and of long-term redistribution of water In response to gravitational and potential gradients in the profile. Redistribution accounted for 60% of the water loss in the soil beneath the seed zone from mid-July to early August, and accounted for none of the loss from early August to early September. Planting date had a significant effect on yield of both wheat and barley; the optimum planting dates were late September to early October. On each planting date, the seeds were placed in moist soil and covered with approximately 5 cm of soil with a deep furrow drill, so temperature was the primary factor affecting rate of first and 70% emergence. Regression equations of rate of emergence on average 10-cm soil temperature from planting to emergence were highly significant. The degree days needed for first and 70% emergence for wheat were 149 and 210 using a base temperature of 0.7 and 0.4 C, respectively, and for barley were 92 and 159 using base temperatures of 6.1 and 3.5 C, respectively. Soil temperatures from 1963 to 1977 were used to develop a means of predicting average daily 10-cm soil temperature. Using this long-term average and the regression equations of rate of emergence and stand establishment versus temperature, the average last date to plant and still obtain 70% stand in 14 days was 25 September. If seeding is delayed until 15 October, lower soil temperatures will cause the average days to 70% stand of wheat to approach 22-24 days, while barley will require 24 - 2 9 days to reach 70% stand at these temperatures

Managing the Rotation from Alfalfa to Corn

This archival publication may not reflect current scientific knowledge or recommendations. Current information available from the University of Minnesota Extension: https://www.extension.umn.edu.This bulletin describes management practices for alfalfa termination and the two subsequent corn crops that will help utilize the benefits of alfalfa.This publication was funded by the Minnesota Agricultural Fertilizer Research and Education Council. The research summarized in this publication was supported by the Minnesota Agricultural Fertilizer Research and Education Council, the Minnesota Corn Research and Promotion Council, the North Central Region-Sustainable Agriculture Research and Education Program, the Minnesota Agricultural Water Resource Center, the Hueg-Harrison fellowship, the University of Minnesota, and the USDA-Agricultural Research Service

Perennial Forages as Second Generation Bioenergy Crops

The lignocellulose in forage crops represents a second generation of biomass feedstock for conversion into energy-related end products. Some of the most extensively studied species for cellulosic feedstock production include forages such as switchgrass (Panicum virgatum L.), reed canarygrass (Phalaris arundinacea L.), and alfalfa (Medicago sativa L.). An advantage of using forages as bioenergy crops is that farmers are familiar with their management and already have the capacity to grow, harvest, store, and transport them. Forage crops offer additional flexibility in management because they can be used for biomass or forage and the land can be returned to other uses or put into crop rotation. Estimates indicate about 22.3 million ha of cropland, idle cropland, and cropland pasture will be needed for biomass production in 2030. Converting these lands to large scale cellulosic energy farming could push the traditional forage-livestock industry to ever more marginal lands. Furthermore, encouraging bioenergy production from marginal lands could directly compete with forage-livestock production

Effect of Manure vs. Fertilizer Inputs on Productivity of Forage Crop Models

Manure produced by livestock activity is a dangerous product capable of causing serious environmental pollution. Agronomic management practices on the use of manure may transform the target from a waste to a resource product. Experiments performed on comparison of manure with standard chemical fertilizers (CF) were studied under a double cropping per year regime (alfalfa, model I; Italian ryegrass-corn, model II; barley-seed sorghum, model III; and horse-bean-silage sorghum, model IV). The total amount of manure applied in the annual forage crops of the model II, III and IV was 158, 140 and 80 m3 ha−1, respectively. The manure applied to soil by broadcast and injection procedure provides an amount of nitrogen equal to that supplied by CF. The effect of manure applications on animal feeding production and biochemical soil characteristics was related to the models. The weather condition and manures and CF showed small interaction among treatments. The number of MFU ha−1 of biomass crop gross product produced in autumn and spring sowing models under manure applications was 11,769, 20,525, 11,342, 21,397 in models I through IV, respectively. The reduction of MFU ha−1 under CF ranges from 10.7% to 13.2% those of the manure models. The effect of manure on organic carbon and total nitrogen of topsoil, compared to model I, stressed the parameters as CF whose amount was higher in models II and III than model IV. In term of percentage the organic carbon and total nitrogen of model I and treatment with manure was reduced by about 18.5 and 21.9% in model II and model III and 8.8 and 6.3% in model IV, respectively. Manure management may substitute CF without reducing gross production and sustainability of cropping systems, thus allowing the opportunity to recycle the waste product for animal forage feeding

Iowa Crop Variety Yield Testing: A History and Annotated Bibliography

Variety testing by U.S. agricultural universities, often in cooperation with experiment stations, and professional crop associations is recognized as an independent, unbiased validation of the viability of commercial crop varieties. In Iowa, variety testing has also been conducted by many private agricultural companies and individual farmers. Records for crop variety evaluations within the state can be traced back to 1871, well before the creation of the Iowa Agricultural Experiment Station in 1888. The Iowa Corn Yield Test (ICYT) is undeniably the most famous of the Iowa variety yield trials; however, corn (Zea mays L.) varieties were being tested long before that program was initiated. Furthermore, Iowa researchers have been conducting variety yield tests on many other field crops. Knowledge of how Iowa variety tests have been organized and published could be helpful to researchers looking for similar, long-term evaluations from other states and around the world. Variety tests from the past also have the potential to help guide new research efforts and may provide an important untapped resource for unique varietal data. As crop scientists and agronomists look to find new sources for biofuels, bio-products, and other industrial uses for various crops, data from historical varieties could be useful. The objective for this review is to provide an historic account with sections on varietal testing in Iowa. It is presented in chronological order followed by sections devoted to specific crops. A Supplemental Information file containing a detailed annotated bibliography is also provided