A factorization of a super-conformal map

A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a meromorphic function. Analogs of the Liouville theorem, the Schwarz lemma, the Schwarz-Pick theorem, the Weierstrass factorization theorem, the Abel-Jacobi theorem, and a relation between zeros of a minimal surface and branch points of a super-conformal map are obtained.Comment: 21 page

Evaluation of metals that are potentially toxic to agricultural surface soils, using statistical analysis, in northwestern Saudi Arabia

© 2015, Springer-Verlag Berlin Heidelberg. Heavy metals in agricultural soils enter the food chain when taken up by plants. The main purpose of this work is to determine metal contamination in agricultural farms in northwestern Saudi Arabia. Fifty surface soil samples were collected from agricultural areas. The study focuses on the geochemical behavior of As, Cd, Co, Cr, Cu, Hg, Pb and Zn, and determines the enrichment factor and geoaccumulation index. Multivariate statistical analysis, including principle component analysis and cluster analysis, is also applied to the acquired data. The study shows considerable variation in the concentrations of the analyzed metals in the studied soil samples. This variation in concentration is attributed to the intensity of agricultural activities and, possibly, to nearby fossil fuel combustion activities, as well as to traffic flows from highways and local roads. Multivariate analysis suggests that As, Cd, Hg and Pb are associated with anthropogenic activities, whereas Co, Cr, Cu and Zn are mainly controlled by geogenic activities. Hg and Pb show the maximum concentration in the analyzed samples as compared to the background concentration