The aim of this paper is to investigate the numerical solutions of delayed fractional differential equations (FDEs). A constant time delay is taken in the Caputo derivative of the state variable and also in the state variable. To obtain solutions, we extend the block boundary value method (BBVM) and show the convergence of the resulting scheme. Further, it is found that the order of convergence is min{m,q-δ +1} , where m and q are the order and block-size of the BBVM, respectively, and δ lies in between 0 and 1. In our methodology, we approximate the fractional order derivative (FoD) by a combination of the m^th -order BBVM and a q^th -order Lagrange interpolating polynomial. Lastly, we analyze the global stability of the numerical scheme and with the aid of some numerical examples, its computational effectiveness is proved. In examples, we analyze some fractional order delay differential systems and present a comparison of solutions for different FoDs. Furthermore, it is demonstrated that the global errors diminish as the FoD decreases, and this fact is supported by the theoretical order of convergence.

This article evaluates a novel class of non-autonomous differential systems involving instantaneous and non-instantaneous impulses in Hilbert spaces. Initially, we investigate the presence of a mild solution for the aforementioned system under some simple conditions on the system parameters. Next, we constructed a new set of sufficient hypotheses for investigating the approximate controllability of the nonlinear system. The evolution operator and fixed point method are frequently employed to justify the existence of a solution. At the end, an example is given to illustrate and validate the proposed theory.

This paper investigates the results concerning the approximate numerical solutions of the non-integer differential equations with multiple delays. The multiple delays may not lie on the same mesh, so in this paper the aim is to deal with such delays using a uniform mesh. The derivative taken in the differential equation is the Caputo fractional derivative of arbitrary order. Our methodology is a combination of the Haar wavelet collocation method (HWCM) and the Lagrange interpolation. In the HWCM, the derivative inside the integral of the fractional derivative is taken to be in the form of an infinite series of the Haar functions, and then a numerical approximation of the infinite sum is taken. The Lagrange interpolating polynomial is used to make approximations of the delays so that we can work with the mesh given by the HWCM. The proposed scheme is found to be convergent and its numerical efficiency is demonstrated with the help of several examples. The error in L_2 norm and L_∞ norm are used to show the numerical accuracy of the methods. The numerical simulations are compared with existing results in the literature.

[This corrects the article DOI: 10.1371/journal.pone.0305582.].

The qualitative study of stochastic fractional nonautonomous systems in infinite-dimensional spaces is rarely available in the literature. Our aim in this article is to examine the existence and sensitivity of a mild solution for a novel class of nonautonomous stochastic fractional differential inclusions driven by standard and fractional Brownian motion (fBm). We derive the existence and uniqueness of the solution for the considered system with the help of operators generated by the probability density function and the family of linear, closed operators by utilizing the Picard iteration method. Furthermore, we investigate the sensitivity of the mild solution concerning the initial condition. The obtained results are proved under weaker assumptions than the Lipschitz conditions on the system parameters. We also use the Jensen, the Gronwall, and the Bihari inequalities to acquire the results. Our results generalize the work corresponding to fractional autonomous and deterministic systems. Lastly, two examples are constructed to validate the produced results.

Oxidative steam reforming is employed to examine the thermodynamic feasibility of the production of hydrogen using propanol as a biomass substrate. For process simulation, the R-Gibbs reactor tool in Aspen Plus is used to check the effects of process variables such as pressure (1-10 atm), temperature (300-1000 K) and molar feed ratio (f1 = steam to propanol = 1-10 and f2 = oxygen to propanol = 0.25-1) on hydrogen production. After sensitivity analysis, the maximum hydrogen is found at 1 atm, 573 K, f1 = 10 & f2 = 0.25. Under the same conditions, the generation of other products such as methane, carbon dioxide, carbon monoxide and carbon (solid) is also analysed. The same optimal operating conditions of process variables are also used to obtain the thermal efficiency of this reforming.

The study of the qualitative attributes of fractional non-autonomous stochastic differential systems is rarely available in the literature. This research work investigates the solvability and Ulam–Hyers stability of non-autonomous fractional differential equations involving standard Brownian motion and fractional Brownian motion (fBm). We describe a mild solution of the considered fractional non-autonomous system through the operators generated by a family of closed linear operators and the probability density function. The existence of a mild solution is established by utilizing the successive approximation approach. Furthermore, we investigate the Ulam–Hyers stability of the considered equation. Our findings are established under Lipschitz conditions on the system parameters, leveraging Borel-Cantelli’s Lemma, Gronwall’s, and Chebyshev’s inequalities. Finally, we present an example to validate our results.

Conventional sheet metal forming processes have problems like low formability, non-uniform strain distribution, spring back, wrinkling, etc. High velocity processes like electrohydraulic forming can deform sheets at high strain rate and have capability to tackle such problems associated with conventional forming operations to a greater extent. Forming limit diagram (FLD) characterizes sheet deformation as measure of formability. Punch stretch test (PST) can assess formability of sheet in conventional low strain rate process, but no standard method is available to determine FLD at high strain rate. So in the present work, an experimental setup has been developed to characterize sheets at high strain rate using hydraulic forming process with a 40 kJ capacitor bank. A similar corresponding standard setup for punch stretch test is also developed for comparative study of formability with respect to dome height, forming limit curve, and strain distribution. Formability of aluminum alloy AA5754 is determined at quasi-static and high strain rates, and comparative analysis is reported for whole state of strain using dog bone samples of width ranging from 10 to 120 mm. An estimate of electrohydraulic forming parameters for high strain test of the Al alloy using the given setup is also determined. Study of comparative strain distribution behavior of samples of different widths is also carried out. Comparative analysis shows that there is an improvement in formability and strain distribution behavior of the alloy deformed using EHF as compared to PST.

Background A death certificate is an important document that serves as a tool for gathering epidemiological data and as an essential legal document. Although it is a mandatory document to be given for all deaths, the quality of its filling is often an ignored aspect and errors are frequently encountered. This documentation process can be mastered with minimal educational efforts. This study aimed to determine the utility of an educational measure in improving the accuracy of death certificate documentation. Methods and materials This pre- and post-interventional study was conducted at Maharaja Agrasen Medical College, Agroha, a tertiary care teaching hospital in Hisar, Haryana, India, wherein an audit of death certificates was done before and after an educational intervention on doctors responsible for filling death certificates. Errors in the death certificates were classified into major and minor errors and compared in the pre- and post-intervention groups. Results A total of 184 pre-intervention and 136 post-intervention death certificates were audited. In the pre-intervention certificates, at least one major and one minor error were present in 88% and 92.93% of the certificates, respectively, which was reduced to 33% (p < 0.01; relative risk (RR) = 3.62; 95% confidence interval (CI) = 2.69-4.91) and 38% (p < 0.01; RR = 3.33; 95% CI = 2.53-4.37), respectively, post-intervention. Reduction in all types of major and minor errors was statistically significant (p < 0.05). Conclusions Errors in death certification are a common but frequently ignored problem that can have a negative impact on epidemiological data and can be drastically reduced with simple educational measures, which need to be carried out regularly.

It is comprehended that the systems without any limitation on their Zeno action are enthralled in a vast class of hybrid systems. This article is influenced by a new category of nonautonomous second‐order measure differential problems with state‐dependent delay (SDD) and noninstantaneous impulses (NIIs). Some new sufficient postulates are created that guarantee the solvability and approximate controllability. We employ the fixed point strategy and theory of Lebesgue–Stieltjes integral in the space of piecewise regulated functions. The measure of noncompactness is applied to establish the existence of a solution. Moreover, the measured differential equations generalize the ordinary impulsive differential equations. Thus, our findings are more prevalent than that encountered in the literature. At last, an example is comprised that exhibits the significance of the developed theory.

Poor dietary intake or unhealthy lifestyle contributes to various health disorders, including postprandial hyperglycemia, leading to type 2 diabetes mellitus (T2DM). Reduction of postprandial glucose concentrations through diet is a key strategy for preventing and managing T2DM. Thus, it is essential to understand how dietary components affect glycemic regulation. Dietary polyphenols (DPs), such as anthocyanins and other phenolics found in various fruits and vegetables, are often recommended for their potential health benefits, although their systemic effectiveness is subject to ongoing debate. Therefore, this review assesses the current and historical evidence of DPs bioactivities, which regulate crucial metabolic markers to lower postprandial hyperglycemia. Significant bioactivities such as modulation of glucose transporters, activation of AMP kinase, and regulation of incretins are discussed, along with prospects for diet-induced therapeutics to prevent the onset of T2DM.

Experimental and numerical studies have been conducted in an enclosure of size 4m x 4m x 4m to determine burning characteristics and the thermal environment inside the closed enclosure. The fire source is a 60 cm diameter isopropanol fuel placed in the center of the enclosed space. The thermal environment was measured along the enclosure's heights and at the longitudinal orientation of the ceiling. The highest temperatures recorded at roof locations C1, C6, C11, and C16 were 175 degrees C, 182 degrees C, 190 degrees C, and 177 degrees C, respectively. Initially, the mass loss rate increased with time, reaching a maximum value of 25.5 g/m2 2 s before decreasing with time. The rate of release of energy is a key parameter that needs to be known for the proper design of the fire protection system. In the present study, the enthalpy balance method was used to predict the rate of heat release. The maximum deviation of heat release rate between the experimental and predicted enthalpy balance was found to be about 20%. Energy transfer to the enclosure surfaces was found to occur at a rate of about 91.2% of the total energy released, whereas energy transfer to gases occurred at a rate of 9.8% of the total energy losses. Numerical studies were performed using the Fire Dynamic Simulator (FDS) to investigate the local characteristics of fires. Isopropanol's Limiting Oxygen Concentration (LOC) was found to be 11 vol.% under stoichiometric conditions. The self-extinction time was observed at 840 s from the ignition which is in good agreement with the semi-empirical equation proposed at different studies.

BACKGROUND:Tuberculosis is a serious life-threatening disease among the top global health challenges and rapid and effective diagnostic biomarkers are vital for early diagnosis especially given the increasing prevalence of multidrug resistance. METHODS:Two human whole blood microarray datasets, GSE42826 and GSE42830 were retrieved from publicly available gene expression omnibus (GEO) database. Deregulated genes (DEGs) were identified using GEO2R online tool and Gene Ontology (GO), protein-protein interaction (PPI) network analysis was performed using Metascape and STRING databases. Significant genes (n = 8) were identified using T-test/ANOVA and Molecular Complex Detection (MCODE) score ≥10, which was validated in GSE34608 dataset. The diagnostic potential of three biomarkers was assessed using Area Under Curve (AUC) of Receiver Operating Characteristic (ROC) plot. The transcriptional levels of these genes were also examined in a separate dataset GSE31348, to monitor the patterns of variation during tuberculosis treatment. RESULTS:A total of 62 common DEGs (57 upregulated, 7 downregulated genes) were identified in two discovery datasets. GO functions and pathway enrichment analysis shed light on the functional roles of these DEGs in immune response and type-II interferon signaling. The genes in Module-1 (n = 18) were linked to innate immune response, interferon-gamma signaling. The common genes (n = 8) were validated in GSE34608 dataset, that corroborates the results obtained from discovery sets. The gene expression levels demonstrated responsiveness to Mtb infection during anti-TB therapy in GSE31348 dataset. In GSE34608 dataset, the expression levels of three specific genes, GBP5, IFITM3, and EPSTI1, emerged as potential diagnostic makers. In combination, these genes scored remarkable diagnostic performance with 100% sensitivity and 89% specificity, resulting in an impressive Area Under Curve (AUC) of 0.958. However, GBP5 alone showed the highest AUC of 0.986 with 100% sensitivity and 89% specificity. CONCLUSIONS:The study presents valuable insights into the critical gene network perturbed during tuberculosis. These genes are determinants for assessing the effectiveness of an anti-TB response and distinguishing between active TB and healthy individuals. GBP5, IFITM3 and EPSTI1 emerged as candidate core genes in TB and holds potential as novel molecular targets for the development of interventions in the treatment of TB.

Introduction: Antibiotic resistance presents a significant global health threat to modern medicine. The awareness and attitude of future doctors undergoing training may play a crucial role in addressing this important issue, influencing the control of resistance and promoting responsible antibiotic stewardship. This study aimed to estimate knowledge, attitudes, and practices regarding antibiotic usage and antimicrobial resistance among tertiary care teaching hospital medical interns. Methodology: The questionnaire-based cross-sectional study was conducted on 123 MBBS interns from multiple medical institutions. Intern's knowledge, attitudes, and self-reported practices regarding antibiotic use were recorded. Results: Based on survey responses from 123 participants, 116 (94.31%) were aware of the adverse effects of indiscriminate antibiotic use, recognizing the risks of ineffective treatment, increased adverse effects, prolonged illness, bacterial resistance, and higher medical costs. Most (106, 86.18%) acknowledged the challenges of treating antibiotic-resistant infections, and 69 (56.10%) correctly identified that bacteria are not a cause of the common cold and flu. Most (115, 93.5%) recognized antibiotic resistance as a significant global health problem. In attitude, 90 (73%) believed antibiotics should be avoided for colds, but 80 (65%) thought they hastened fever recovery. Only 48 (39%) recognized that antibiotics contribute to resistance, while 102 (83%) agreed skipping doses fosters resistance. Most support hospital policies (118, 96%) and curriculum courses (112, 91%) for rational antibiotic use. Regarding practice, 12 (9.76%) interns admitted to overusing antibiotics, 68 (55.28%) consulted a doctor before starting antibiotics, and 87 (70.73%) checked expiry dates. Additionally, 62 (50.41%) preferred antibiotics for cough and sore throat symptoms. Conclusions: The study highlights that while interns have a good knowledge and awareness of the harms of antibiotic misuse, they are not translating this knowledge into practice. This indicates a disconnect between understanding and application. Therefore, there is a need to add a rational antibiotic prescription and stewardship module to the medical curriculum to ensure that knowledge is effectively translated into changing beliefs and practices.

BACKGROUND:Umbilical cord milking (UCM) and delayed cord clamping (DCC) are strategies that improve the hemodynamic condition of the newborn and also increase the storage of iron. This study aimed to compare the effects of DCC with or without milking in late preterm and term neonates at different time intervals after birth (60, 120, and 180 seconds) on hematological and hemodynamic parameters in neonates at six weeks of age.MATERIALS AND METHODS:In this double-arm, parallel-group, triple-blind, and active-controlled trial, all 150 eligible neonates were randomized with allocation concealment into three groups: Group A (DCC with UCM at 60 seconds), Group B (DCC with UCM at 120 seconds), and Group C (only DCC for 180 seconds). Hemodynamic parameters were recorded and compared during the first 48 hours, and hematological parameters were compared at six weeks of age.RESULTS:At six weeks, a significant difference in hemoglobin levels was noted between Groups A, B, and C (p<0.001). The difference in serum ferritin values at six weeks was also statistically significant in comparisons across all three groups (p=0.003). Regarding secondary outcomes examined, hemodynamic parameters and the incidence of neonatal hyperbilirubinemia were found to be comparable at 48 hours after birth.CONCLUSION:DCC followed by UCM at 120 seconds and DCC till 180 seconds proves superior to DCC with UCM at 60 seconds in preserving elevated hemoglobin levels and iron stores in neonates at six weeks of age. DCC for 180 seconds yielded comparable results, followed by UCM at 120 seconds. All three methods are considered safe and effective without compromising the neonate's hemodynamics.

Objective: Pharmacogenomics plays an important role in drug metabolism. A stable anticoagulation is important for primary and secondary prevention of cardioembolic stroke and cerebral venous sinus thrombosis (CVST). We report the role of cytochrome P450 (CYP2C9*2/*3) and vitamin K epoxide reductase subunit 1 (VKORC1) genotypes and acquired causes in maintaining stability of anticoagulation following acenocoumarin in cardioembolic stroke and CVST. Methods: The study comprised 157 individuals with cardioembolic stroke and CVST who were on acenocoumarin. Their comorbidities, comedication, and dietary habits were noted. Prothrombin time and international normalized ratio (INR) were measured during follow-up, and the coagulation status was categorized as stable (>50% occasions in therapeutic range) and unstable (>50% below and above therapeutic range). Genotyping of VKORC1, CYP2C9*2, and CYP2C9*3 was done by polymerase chain reaction-restriction fragment length polymorphism. Bleeding and embolic complications were noted. The predictors of unstable INR were evaluated using multivariate analysis. Results: INR was stable in 47.8% and unstable in 52.2% of patients. Patients with mutant genotypes required low dose of acenocoumarin. The predictors of unstable INR were metallic valve (odds ratio [OR] 4.07, 95% confidence interval [CI] 1.23–13.49, P = 0.02), use of digoxin (OR 0.031, 95% CI 0.13–0.74, P = 0.09), proton pump inhibitor (OR 0.23, 95% CI 0.06–0.91, P = 0.037), sodium valproate (OR 0.22, 95% CI 0.05–0.85, P = 0.029), and CYP2C9*2 genotype (OR 5.57, 95% CI 1.19–26.06, P = 0.02). Conclusions: Variant genotypes of VKORC1, CYP2C9*2, and CYP2C9*3 required lower dose of acenocoumarin, and CYP2C9*2 was associated with unstable INR. Comedication is a modifiable risk factor that needs attention.

This article contemplates a non-autonomous nonlinear differential system in a separable Hilbert space 𝒳 . The projection operators are used to confine our concern to a finite-dimensional subspace of 𝒳 . The existence, uniqueness, and convergence of approximate solutions are explored by making use of the hypothesis of fractional powers of a closed linear operator. We also analyze the Faedo–Galerkin approximation of the solution. An example is also built to exhibit the significance of the acquired results.

This manuscript is devoted to the approximate controllability of semilinear infinite-delayed stochastic differential inclusions involving impulses. The presence of a mild solution for the aforementioned system is shown by employing the theory of stochastic analysis and the fixed point theorem due to Covitz and Nadler. Then, we construct a group of sufficient conditions and utilize Grownwall's inequality to establish the approximate controllability results. Finally, two examples are constructed to exemplify the feasibility of derived outcomes.

Control systems in which instantaneous and noninstantaneous impulses occur simultaneously are difficult to handle. In this article, we investigate the solvability and approximate controllability for a new category of stochastic differential equations steered by Poisson jumps with instantaneous and noninstantaneous impulses. Utilizing the theory of fundamental solution, stochastic analysis, the measure of noncompactness, and the fixed-point approach, we establish the presence of a mild solution for the proposed system. We have also constructed a new set of sufficient constraints that assures approximate controllability of the considered system. Next, we discuss the existence of a solution and approximate controllability for an impulsive deterministic control system in which the nonlinear term contains spatial derivatives. Lastly, two examples are presented to encapsulate the abstract results.