Coupled Fixed Point Theorem for Weakly Compatible Mappings in Menger Spaces

In this paper, first, we introduce the notion of weakly compatible maps for coupled maps and then prove a coupled fixed point theorem under more general t-norm(H-type norm) in Menger spaces. We support our theorem by providing a suitable example. At the end, we obtain an application.

Artificial neural network based modeling of liquid membranes for separation of dysprosium

In recent years,the liquid membrane process has been widely investigated to remove rare earth metals.However,transport modeling of this process requires the accurate values of several parameters,which are difficult to measure.Thus,the accurate simulation of this process is a challenging task.In this study,the artificial neural network(ANN)based approach is used to model the liquid membrane process for removing dysprosium.Experimental results from a previous study were used to train the ANN.Initially,the number of neurons in the hidden layer was optimized.The minimum mean squared error between experimental results and model predictions is found with ten neurons.Model predictions were successfully validated with experimental results with correlation factor(R)of 0.9987,which confirms the authenticity of the trained network.Trained ANN was then used to study the effects of different operating parameters on transport rate.The higher volume ratio of membrane solution to feed solution(3-4)with 50-60 min of operation,higher feed pH(5),HCl concentration in stripping solution of 2 mol/L,and moderate concentration of carrier species(0.5 mol/L)with 0.5×10^(-4) mol/L dysprosium initial concentration are found to be optimum values of operating conditions for maximizing the transport rate.

Exciton fine structure in twisted transition metal dichalcogenide heterostructures

Moirésuperlattices of transition metal dichalcogenide(TMD)heterostructures give rise to rich excitonic phenomena associated with the interlayer twist angle.Theoretical calculations of excitons in such systems are typically based on model moirépotentials that mitigate the computational cost.However,predictive understanding of the electron-hole coupling dominating the excitations is crucial to realize the twist-induced modifications of the optical selection rules.In this work,we use many-body perturbation theory to evaluate the relation between twist angle and exciton properties in TMD heterostructures.We present an approach for unfolding excitonic states from the moiréBrillouin zone onto the separate-layer ones.Applying this method to a large-angle twisted MoS^(2)/MoSe^(2) bilayer,we find that the optical spectrum is dominated by mixed electron–hole transitions with different momenta in the separate monolayers,leading to unexpected hybridization between interlayer and intralayer excitons.Our findings offer a design pathway for exciton layer-localization in TMD heterostructures.

Prediction of significant hyperbilirubinemia in term neonates by early non-invasive bilirubin measurement

Background:Neonatal jaundice is a common problem.We evaluated the utility and best cut-off values of 24-and 48-hour transcutaneous bilirubin indices (TcBI) in predicting subsequent significant hyperbilirubinemia and evaluated various associated maternal and fetal risk factors.Methods:TcBI at 24 and 48 hours and serum bilirubin levels at 72 hours of age were obtained for healthy,term,appropriate for gestational age neonates.Neonates with prematurity,birth weight <2500 g,ABO or Rh incompatibility,onset of clinical jaundice <24 hours,clinical suspicion of septicemia,positive pressure ventilation at birth,admission in neonatal intensive care unit and contraindications for BiliChek were excluded.Twently-four and 48-hour TcB indices were assessed as predictors of subsequent hyperbilirubinemia,defined as serum bilirubin >17 mg/dL after 72 hours of life and various cut-offs,and were evaluated by calculating sensitivity,specificity and predictive values.Results:Of 500 newborns,4.6% had significant hyperbilirubinemia,27% had TcBI (mg/dL) <5 at 24 hours,and 27.4% had TeBI <8 at 48 hours.None of them had subsequent hyperbilirubinemia (100% negative predictive value).The percentage of newborns with subsequent hyperbilirubinemia increased from 3.4% to 13.2% as their 24-hour TcBI increased from 6 to above 9 mg/dL and from 4.2% to 7.4% as their 48-hour TcBI increased from 8 to above 11 mg/dL.The best cut-off value was TcBI (mg/dL) 7 (odd ratio=4.86,95% confidence interval:1.66-15.22) at 24 hours and 10 (odd ratio=2.87,95% confidence interval:1.04-8.29) at 48 hours.Area under the receiver operating characteristic curve for 24-and 48-hour measurements was 0.750 and 0.715,respectively.Maternal premature rupture of membranes,deep transverse arrest,post-date pregnancy,and fetal distress were significant risk factors for hyperbilirubinemia.Conclusions:Twenty-four and 48-hour TcB indices are good predictors of subsequent hyperbilirubinemia.Twenty-four-hour TcBI had better predictive ability than 48-hour TcBI.