In this paper, we proposed new results in quadruple Laplace transform and proved some properties concerned with quadruple Laplace transform. We also developed some applications based on these results and solved homogeneous as well as non-homogeneous partial differential equations involving four variables. The performance of quadruple Laplace transform is shown to be very encouraging by concrete examples. An elementary table of quadruple Laplace transform is also provided.

Abstract:The use of inverse methods allow efficient model calibration. This study employs PEST to calibrate a large catchment scale transient flow model. Results are demonstrated by comparing manually calibrated approaches with the automated approach. An advanced Tikhonov regularization algorithm was employed for carrying out the automated pilot point (PP) method. The results indicate that automated PP is more flexible and robust as compared to other approaches. Different statistical indicators show that this method yields reliable calibration as values of coefficient of determination (R 2 ) range from 0.98 to 0.99, Nash Sutcliffe efficiency (ME) range from 0.964 to 0.976, and root mean square errors (RMSE) range from 1.68 m to 1.23 m, for manual and automated approaches, respectively. Validation results of automated PP show ME as 0.969 and RMSE as 1.31 m. The results of output sensitivity suggest that hydraulic conductivity is a more influential parameter. Considering the limitations of the current study, it is recommended to perform global sensitivity and linear uncertainty analysis for the better estimation of the modelling results.

Nitrate in groundwater is a major concern in agricultural sub-watersheds. This study assessed the impacts of future climate and agricultural land use changes on groundwater nitrate concentrations in an agricultural sub-watershed (Norfolk site) in southern Ontario, Canada. A fully integrated hydrologic model (HydroGeoSphere) was used in combination with the root zone water quality model (RZWQM2) (shallow zone) to develop water flow and nitrate transport models. Three climate change models and three crop rotations (corn-soybean rotation, continuous corn, corn-soybean-winter wheat-red clover rotation) were used to evaluate the potential impact on groundwater quality (nine predictive scenarios). The selected climate change scenarios yielded less water availability in the future period than in the reference period (past conditions). The simulated nitrate nitrogen (Nitrate-N) concentrations were lower during the future period than the reference period. The continuous corn land use scenario produced higher Nitrate-N concentrations compared to the base case (corn-soybean rotation). However, the best management practices (BMP) scenario (corn-soybean-winter wheat-red clover rotation) produced significantly lower groundwater nitrate concentrations. BMPs, such as the one examined herein, should be adopted to reduce potential negative impacts of future climate change on groundwater quality, especially in vulnerable settings. These findings are important for water and land managers, to mitigate future impacts of nutrient transport on groundwater quality under a changing climate.

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Leishmaniasis, a protozoan parasitic pathology, is caused by infection with a parasite known as Leishmania donovani, which is transmitted to humans through the bite of a sand fly. The disease has various manifestations, including cutaneous leishmaniasis, visceral leishmaniasis (VL), and disseminated cutaneous leishmaniasis. Visceral leishmaniasis (VL), also known as kala-azar, is mostly seen in the Asian and African regions and can be deadly if left untreated. We present the case of a 10-month-old male infant who was brought to the office with the chief complaints of recurrent fever for the past one month, along with generalized fatigue and poor feeding. A comprehensive history, detailed physical examination, and laboratory testing, including bone marrow aspiration, were performed, and visceral leishmaniasis was diagnosed.