We investigate the existence of multiple positive solutions to the nonlinear q-fractional boundary value problem c D a q u t a t f u t 0, 00, by using a fixed point theorem in a cone.
ObjectivesIn preterm infants, hyperbilirubinemia is common and can impair the central nervous system. The tests available for measuring bilirubin is to collect blood from heel pricking and occasionally taking blood samples from inserted cannulas, which is painful. Therefore, there is a need to develop a non-invasive device to detect bilirubin levels in newborns and interpret the severity of jaundice.MethodsWe conducted a cross-sectional study of 100 neonates. Patient data was collected between June 2015 and December 2016 from King Khalid Hospital at Al-Majma’ah, Saudi Arabia, and Alpine Hospital, Gurgaon, India. The mean gestational age of neonates was 39.0 weeks. Total bilirubin was measured using a transcutaneous bilirubinometer on the forehead and obtaining optical imaging through scanning of conjunctiva of eyes, also referred to as BiliChek and BiliCapture, respectively. Later the blood samples were obtained from these patients and tested in the laboratory to determine total serum bilirubin (TSB) levels.ResultsThe concentration of bilirubin as measured from serum, BiliChek, and BiliCapture were 10.7±2.0, 11.6±2.7, and 13.1±2.3 mg/dL, respectively. Correlation was high between TSB and BiliChek (r2 = 0.88) and between TSB and BiliCapture (r2 = 0.73). The Bland-Altman plots showed good agreement when comparing bilirubin values for both BiliChek and BiliCapture devices. Bilirubin measurement was further checked for the sensitivity and specificity and was 88.0% and 76.0% using BiliChek and 92.0% and 75.6% using BiliCapture, respectively.ConclusionsThe optical imaging of conjunctiva for bilirubin assay is a safe alternative to a laboratory bilirubin assay and transcutaneous bilirubinometer BiliChek.
The stochastic (2+1)-dimensional breaking soliton equation (SBSE) is considered in this article, which is forced by the Wiener process. To attain the analytical stochastic solutions such as the polynomials, hyperbolic and trigonometric functions of the SBSE, we use the tanh–coth method. The results provided here extended earlier results. In addition, we utilize Matlab tools to plot 2D and 3D graphs of analytical stochastic solutions derived here to show the effect of the Wiener process on the solutions of the breaking soliton equation.
This article considers the stochastic fractional Radhakrishnan-Kundu-Lakshmanan equation (SFRKLE), which is a higher order nonlinear Schrödinger equation with cubic nonlinear terms in Kerr law. To find novel elliptic, trigonometric, rational, and stochastic fractional solutions, the Jacobi elliptic function technique is applied. Due to the Radhakrishnan-Kundu-Lakshmanan equation’s importance in modeling the propagation of solitons along an optical fiber, the derived solutions are vital for characterizing a number of key physical processes. Additionally, to show the impact of multiplicative noise on these solutions, we employ MATLAB tools to present some of the collected solutions in 2D and 3D graphs. Finally, we demonstrate that multiplicative noise stabilizes the analytical solutions of SFRKLE at zero.
The space-fractional stochastic approximate long water wave equation (SFSALWWE) is considered in this work. The Riccati equation method is used to get analytical solutions of the SFSALWWE. This equation has never been examined with stochastic term and fractional space at the same time. In general, the noise term that preserves the symmetry reduces the domain of instability. To check the impact of Brownian motion on these solutions, we use a MATLAB package to plot 3D and 2D graphs for some analytical fractional stochastic solutions.
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