Complete descriptions of the particle-size distribution (PSD) curve should provide more information about various soil properties as opposed to only the textural composition (sand, silt and clay (SSC) fractions). We evaluated the performance of 19 models describing PSD data of soils using a range of efficiency criteria. While different criteria produced different rankings of the models, six of the 19 models consistently performed the best. Mean errors of the six models were found to depend on the particle diameter, with larger error percentages occurring in the smaller size range. Neither SSC nor the geometric mean diameter and its standard deviation correlated significantly with the saturated hydraulic conductivity (Kfs); however, the parameters of several PSD models showed significant correlation with Kfs. Porosity, mean weight diameter of the aggregates, and bulk density also showed significant correlations with PSD model parameters. Results of this study are promising for developing more accurate pedotransfer functions.
Let $R$ be a prime ring with its Utumi ring of quotients $U$ and extended centroid $C$. Suppose that $F$ is a generalized derivation of $R$ and $L$ is a noncentral Lie ideal of $R$ such that $F(u)[F(u),u]^n=0$ for all $u \in L$, where $n\geq 1$ is a fixed integer. Then one of the following holds: \begin {itemize} \item [(1)] there exists $\lambda \in C$ such that $F(x)=\lambda x$ for all $x\in R$; \item [(2)] $R$ satisfies $s_4$ and $F(x)=ax+xb$ for all $x\in R$, with $a, b\in U$ and $a-b\in C$; \item [(3)] $\mathop {\rm char}(R)=2$ and $R$ satisfies $s_4$. \end {itemize} As an application we also obtain some range inclusion results of continuous generalized derivations on Banach algebras.