Improved Young and Heinz inequalities with the Kantorovich constant

In this article, we study the further refinements and reverses of the Young and Heinz inequalities with the Kantorovich constant. These modified inequalities are used to establish corresponding operator inequalities on Hilbert space and Hilbert-Schmidt norm inequalities.Comment: 11 page

Upper bounds for the spread of a matrix

AbstractIn this paper, we exhibit new and sharper upper bounds of the spread of a matrix

On the Lawson–Lim means and Karcher mean for positive invertible operators

Abstract This note aims to generalize the reverse weighted arithmetic–geometric mean inequality of n positive invertible operators due to Lawson and Lim. In addition, we make comparisons between the weighted Karcher mean and Lawson–Lim geometric mean for higher powers

Green Manure Amendment Increases Soil Phosphorus Bioavailability and Peanut Absorption of Phosphorus in Red Soil of South China

Peanut (Arachis hypogaea L.) is one of the most important crops produced worldwide. Peanut is the dominant crop in the typical upland red soil areas of China; however, phosphorus bioavailability in red soil is very low, which severely affects peanut production. To improve the phosphorus bioavailability, which substantially promotes the green development of peanut production, a peanut–green manure rotation field experiment was conducted with six treatments (milkvetch; radish; brassica rape; mustard rape; winter fallow and no-tillage), commencing in September 2017 in the red soil area of Jiangxi province, China. The results show that compared with no-tillage (NT) treatments, different green manure returning treatments had significant effects on soil pH, soil phosphorus components and available potassium content. The particulate phosphorus and soil available phosphorus contents in the green manure treatments were significantly higher than those in the winter fallow (WF) treatment. Compared with the WF treatment, the content of particulate phosphorous in brassica rape (BR), radish (R) and milkvetch (MV) treatments was significantly increased by 6.55%, 3.66% and 2.50%, respectively; the available phosphorus content in mustard rape (MR), BR, R and MV was significantly increased by 20.93%, 25.60%, 23.76% and 18.10%, respectively. In addition, the total phosphorus content of peanut shell in the MV and R treatment was significantly higher than that in the WF treatment, increasing by 33.47% and 60.66%, respectively. Compared with the WF treatment, the peanut biomass of MR, BR and R treatments increased significantly by 19.51%, 29.83% and 19.77%, respectively. The total phosphorus accumulation in all green manure treatments was higher than that in the WF treatment, and the MV treatment reached a significant level at 18.83%. Based on these results, the particulate phosphorus (PP) and available phosphorus were significantly affected by different green manure treatments; green manure amendment improves peanut phosphorus uptake. The use of green manure (especially milkvetch and brassica rape) can be recommended to improve phosphorus bioavailability and yield of peanut in red soil areas

Green Manure Amendment Can Reduce Nitrogen Fertilizer Application Rates for Oilseed Rape in Maize–Oilseed Rape Rotation

Excessive use of chemical fertilizers has led to a reduction in the quality of arable land and environmental pollution. Using green manure to replace chemical fertilizers is one of the most effective solutions. To study the effect of green manure on the requirement for nitrogen fertilizer in oilseed rape, a field experiment with maize–oilseed rape rotation was conducted. Green manure was intercropped between rows of maize and returned after the maize harvest, with no green manure intercropped as control. Different nitrogen fertilizer treatments (0, 65%, 75% and 100% N rates, respectively) were applied during the oilseed rape season. The results showed that with a 35% reduction in nitrogen application rate, the rapeseed grain yield was significantly higher with the maize intercropping with green manure returned to the field than with the maize monocropping treatment at the same nitrogen level. Under conditions of intercropping and return of green manure, compared with the full standard rate of nitrogen fertilizer treatment, a reduction in nitrogen application of 25–30% in the rape season had no significant effect on rape yield. The agronomic efficiency of nitrogen fertilizer on oilseed rape increased significantly, by 47.61–121%, with green manure incorporation. In addition, green manure incorporation significantly increased the soil organic matter content and the soil-available nitrogen content when chemical nitrogen fertilization was abandoned. Benefit analysis showed that a 25–35% reduction in chemical nitrogen fertilizer applied to oilseed rape crops could be achieved by intercropping green manure in the maize season before the sowing of rapeseed in the experimental area. In the long-term, this measure would increase nitrogen utility, reduce production costs, and have concomitant environmental benefits of improving the quality of cultivated land