No abstract

We study a generalized Abreu equation and derive some estimates.

Summary There is limited information on zinc (Zn2+) adsorption and desorption by different types of soil, especially acidic ones following amendment with manure‐ and lignocellulose‐derived biochars. The novelty of this research is a comparison of the mechanisms of adsorption and desorption of Zn2+ by different types of acidic soil amended with biochar derived from either swine manure or rape straw. Both biochars were prepared at a pyrolysis temperature of 500°C before being incorporated into four types of soil with low pH (pHH2O from 4.61 to 5.91) at an incorporation rate of 3%. Following incubation for 360 days, we carried out batch experiments of Zn2+ adsorption and desorption. The dual‐mode model (DMM) was more suitable for describing the adsorption isotherms of the four soil types following biochar incorporation than the distributed reactivity model (DRM). Swine‐manure biochar enhanced Zn2+ adsorption by soil more than rape‐straw biochar. The increases in Zn2+ adsorption by the different soil types following biochar incorporation were in the order Psammaquent > Plinthudult > Paleudalf > Argiustoll soil, whereas it was most difficult to desorb the Zn2+ already present, in reverse order: Argiustoll > Paleudalf > Plinthudult > Psammaquent soil. This could be attributed to differences in soil pH, organic carbon, cation exchange capacity (CEC) and soil texture. Both non‐electrostatic and electrostatic adsorption mechanisms were identified in the four soil types. The negative surface charge of biochar is responsible for the electrostatic adsorption, whereas functional oxygen groups and mineral components of biochar were responsible for non‐electrostatic adsorption. Non‐electrostatic adsorption was more important for the swine‐manure biochar than for the rape‐straw biochar, which was attributed to the larger content of mineral components (phosphate and silicate anions) of the former. In conclusion, the biochar effects on Zn2+ adsorption depended on the initial Zn2+ concentration, soil pH, soil type and biochar origin.

No abstract

We study a generalized Abreu Equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform Kstability.