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

Source clustering in the Hi-GAL survey determined using a minimum spanning tree method

The aims are to investigate the clustering of the far-infrared sources from the Herschel infrared Galactic Plane Survey (Hi-GAL) in the Galactic longitude range of 71 to 67 deg. These clumps, and their spatial distribution, are an imprint of the original conditions within a molecular cloud. This will produce a catalogue of over-densities. Methods. The minimum spanning tree (MST) method was used to identify the over-densities in two dimensions. The catalogue was further refined by folding in heliocentric distances, resulting in more reliable over-densities, which are cluster candidates. Results. We found 1633 over-densities with more than ten members. Of these, 496 are defined as cluster candidates because of the reliability of the distances, with a further 1137 potential cluster candidates. The spatial distributions of the cluster candidates are different in the first and fourth quadrants, with all clusters following the spiral structure of the Milky Way. The cluster candidates are fractal. The clump mass functions of the clustered and isolated are statistically indistinguishable from each other and are consistent with Kroupa’s initial mass function

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

Exchangeable and Bioavailable Aluminium in the Mountain Forest Soil of Barania Góra Range (Silesian Beskids, Poland)

The research was carried out in the spruce forests of Barania Góra (Silesian Beskids, Poland) affected by pandemic dying of trees. Twenty-seven samples were collected from the O layer in two plots: 17 in a cut down forest infested with insect pests (bark beetle) and ten in a 120-year-old healthy forest. The analyses covered basic parameters (pHH2O, pHKCl, worg, Ctot, Ntot, CEC) and the concentrations of aluminium in the fractions leached with 0.1 M BaCl2 (Alexch), 0.5 M CuCl2 and 0.1 M Na4P2O7 (Albio) solutions. The total aluminium concentration in the soil was assayed digesting samples with hydrofluoric acid. The effect of pH and organic matter content on the amount of exchangeable (Alexch) and bioavailable (Alexch) aluminium in the soil was analysed. It has been found that the soils in both plots are strongly acidic and contain 550 to 1,700 mg kg−1 of exchangeable aluminium and 1,200 to 4,800 mg kg−1 of bioavailable aluminium. The lack of disease symptoms in the spruce trees in plot 2 can be explained by the higher content of organic matter in the soil. Unfortunately, one might expect that the high concentration of exchangeable aluminium will also cause the trees in the area to wither