On the computation of zeros of Bessel functions

The zeros of some chosen Bessel functions of different orders is revised using the well-known bisection method , McMahon formula is also reviewed and the calculation of some zeros are carried out implementing a recent version of MATLAB software. The obtained results are analyzed and discussed on the lights of previous calculations

Diffusion tensor magnetic resonance imaging in the gradingof liver fibrosis associated with congenital ductal plate malformations

Purpose: Liver biopsy is still the standard method for the diagnosis of ductal plate malformations (DPM). However, it is an invasive tool. Magnetic resonance imaging (MRI) has shown its accuracy in the diagnosis of this pathology. Herein, a study was conducted to elucidate the role of diffusion MRI parameters in predicting the degree of hepatic fibrosis. Material and methods: This prospective study included 29 patients with DPM and 20 healthy controls. Both groups underwent diffusion tensor magnetic resonance imaging (DT-MRI), and its parameters were compared between patients and controls, and then they were correlated with the degree of liver fibrosis in the patient group. Results: All patients with DPM, whatever its type, expressed a significantly lower hepatic apparent diffusion coefficient (ADC) compared to controls. However, fractional anisotropy (FA) showed no significant difference between them. The ADC value of 1.65 × 10-3 mm2/s had sensitivity and specificity of 82.1% and 90%, respectively, in differentiating DPM patients from healthy controls. It was evident that patients with higher fibrosis grades had significantly lower hepatic ADC, indicating a negative correlation between ADC and the grade of hepatic fibrosis; rs = -0.901, p < 0.001. Conclusions: DT-MRI showed good efficacy in the diagnosis of congenital DPM. Moreover, ADC could be applied to monitor the degree of liver fibrosis rather than the invasive liver biopsy. No significant correlation was noted between the FA and the grades of liver fibrosis

Prediction of water distribution uniformity of sprinkler irrigation system based on machine learning algorithms

Abstract The coefficients of uniformity Christiansen's uniformity coefficient (CU) and distribution uniformity (DU) are an important parameter for designing irrigation systems, and are an accurate measure for water lose. In this study, three machine learning algorithms Random forest (RF), extreme gradient boosting (XGB) and random forest-extreme gradient boosting (XGB-RF) were developed to predict the water distribution uniformity based on operating pressure, heights of sprinkler, discharge, nozzle diameter, wind speed, humidity, highest and lowest temperature for three different impact sprinklers (KA-4, FOX and 2520) for square and triangular system layout based on four scenarios (input combinations). The main findings were; the highest CU value was 86.7% in the square system of 2520 sprinkler under 200 kPa, 0.5 m height and 0.855 m3/h (Nozzle 2.5 mm). Meanwhile, in the triangular system, it was 87.3% under the same pressure and discharge and 1 m height. For applied machine learning, the highest values of R2 were 0.796, 0.825 and 0.929 in RF, XGB and XGB-RF respectively in the first scenario for CU. Moreover, for the DU, the highest values of R2 were 0.701, 0.479 and 0.826 in RF, XGB and XGB-RF respectively in the first scenario. The obtained results revealed that the sprinkler height had the lowest impact on modeling of the water distribution uniformity