ALBERT

Description: On one hand, we construct λ-symmetries and their corresponding integrating factors and invariant solutions for two kinds of ordinary differential equations. On the other hand, we present μ-symmetries for a (2+1)-dimensional diffusion equation and derive group-reductions of a first-order partial differential equation. A few specific group invariant solutions of those two partial differential equations are constructed.

Description: Rising solid waste production has caused high levels of environmental pollution. Population growth, economic patterns, and lifestyle patterns are major factors that have led to the alarming rate of solid waste production. Generally, solid wastes such as paper, wood, and plastic are disposed into landfills due to its low operation and maintenance costs. However, leachate discharged from landfills could be a problem in surfaces and groundwater if not adequately treated. This study investigated the patterns of the water quality index (WQI) and polycyclic aromatic hydrocarbons (PAH) along Johan River in Perak, Malaysia, which received treated leachate from a nearby landfill. An artificial neural network (ANN) was also applied to predict WQI and PAH concentration of the river. Seven sampling stations were chosen along the river. The stations represented the upstream of leachate discharge, point of leachate discharge, and five locations downstream of the landfill. Sampling was conducted for one year starting July 2018. Physicochemical parameters, namely pH, biological oxygen demand, chemical oxygen demand, ammoniacal nitrogen, total suspended solids, and dissolved oxygen, were used to compute the water quality index (WQI). PAH concentrations were determined by liquid–liquid extraction of water samples followed by an analysis using gas chromatography. Results showed that WQI of Johan River was under Class III where intensive treatment was required to make it suitable for drinking purposes. The highest recorded PAH concentrations were fluoranthene (333.4 ppb) in the dry season and benzo(a) pyrene (93.5 ppb) in the wet season. A correlation coefficient (Rp) for a model prediction based on WQI-ANN and TEC-ANN (toxicity equivalent concentration) in the wet and dry seasons was 0.9915, 0.9431, 0.9999, and 0.9999, respectively. ANN results showed good model performance with Rp ≈ 0.9. This study suggested that ANN is a useful tool for water quality studies.