Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

Geochemical and isotopic evidences from groundwater and surface water for understanding of natural contamination in chronic kidney disease of unknown etiology (CKDu) endemic zones in Sri Lanka

Chronic kidney disease of unknown etiology (CKDu) is the main health issue in the dry zone of Sri Lanka. Despite many studies carried out, causative factors have not been identified yet clearly. According to the multidisciplinary researches carried out so far, potable water is considered as the main causative factor for CKDu. Hence, the present study was carried out with combined isotopic and chemical methods to understand possible relationships between groundwater; the main drinking water source, and CKDu in four endemic areas in the dry zone. Different water sources were evaluated isotopically (²H, ³H and ¹⁸O) and chemically from 2013 to 2015. Results revealed that prevalence of CKDu is significantly low with the groundwater replenished by surface water inputs. It is significantly high with the groundwater stagnated as well as groundwater recharged from regional flow paths. Thus, the origin, recharge mechanism and flow pattern of groundwater, as well as geological conditions which would be responsible for natural contamination of groundwater appear as the main causative factors for CKDu. Therefore, detailed investigations should be made in order to identify the element(s) in groundwater contributing to CKDu. The study recommends providing drinking water to the affected zones using water sources associated with surface waters.     

Spatial and temporal variation in the stable isotope composition (δ18O and δ2H) of rain across the tropical island of Sri Lanka

Seasonal and spatial variation in δ¹⁸O and δ²H in rainwater was determined in three selected transects across Sri Lanka, the tropical island in the Indian Ocean. Local meteoric water lines (LMWLs) for three distinguished climatic zones; wet, dry and intermediate were constructed. LMWLs show slight variations in their gradients and respective d-excess values, depending on the air moisture origin, circulation and environmental conditions of each climatic zone. The elevation effect and amount effect could be identified but the continental effect is not significantly seen in the isotope composition of rain in the concerned areas. The results reasonably revealed that the distinct rainfall regimes; two monsoonal rains and two convectional (inter-monsoon) rains have characteristic isotopic signatures. Also the impact of (i) terrestrial and oceanic moisture sources, (ii) depression and cyclonic conditions of the Bay of Bengal, and (iii) topography of the country on the variation of the isotopic composition of rain in Sri Lanka could be satisfactorily identified.