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Root finding is a basic example that still remnant an interest to several researchers. Several hybrid experiments are developed to obtain approximate solutions for nonlinear equations. Thus, this paper presents an analysis on numerical comparison between common method and the other methods. An evaluation iterative method MATLAB is utilized for this paper. Numerical and interpretative results prove that Dekker’s Formula is acceptably efficient, accurate, and easy to use compared with other iterative methods.

In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams–Bashforth–Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams–Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method.

New three iterative methods in order to solve non-linear problems for PV cell equations with various data of R (load resistance) have been investigated. A series of hybrid algorithms Newton’s, Predictor-Corrector Type (A1), Predictor-Corrector Type (A2) and Dekker’s are implemented to obtain approximate solutions for non-linear functions. The purpose of the present paper is to analysis on numerical comparison between the standard Newton’s algorithm with A1, A2 and DM algorithms. It is evidenced that these methods have nearly eight computations while; the proposed method has six computations per iteration. The Numerical and illustrative results reveal that the new suggested technique (DM) is more accurate, least iterations for convergence than other numerical methods and a computational Matlab 18a is used for this paper.

We introduce a path following algorithm forL_{1}$-regularized generalized linear models. TheL_{1}$-regularization procedure is useful especially because it, in effect, selects variables according to the amount of penalization on theL_{1}$-norm of the coefficients, in a manner that is less greedy than forward selection-backward deletion. The generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor-corrector method of convex optimization. Selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths; we suggest intuitive and flexible strategies for choosing appropriate values. We demonstrate the implementation with several simulated and real data sets.

This article presents a novel control approach using a two‐degree‐of‐freedom (2‐DOF) Smith predictor structure for double integrating plus time delay plants. The PD and PID controllers, integral components of the Smith predictor scheme, serve distinct roles in the control process. The PD controller is responsible for set‐point tracking, while both PD and PID controllers contribute to the rejection of load disturbances. Each controller is designed using the pole placement technique, with an appropriate tuning parameter established to balance performance and robustness effectively. A low‐pass filter is incorporated to improve the response of the set‐point signal by attenuating high‐frequency noise. The proposed method's effectiveness is compared with Skogestad internal model control, a well‐known PID tuning method, to benchmark performance improvements and demonstrate the advantages of the 2‐DOF Smith predictor approach. Simulation and comparison analysis demonstrates that the proposed controller setting is suitable for industrial applications due to its quick set‐point tracking, effective load disturbance rejection, and smooth control signal. The study highlights the practical benefits of the 2‐DOF Smith predictor in enhancing industrial control system performance and suggests directions for future research, including experimental validation and robustness analysis under varying system parameters. This article introduces a novel two‐degree‐of‐freedom Smith predictor structure for controlling double integrating plus time delay plants, utilizing PD and PID controllers for set‐point tracking and load disturbance rejection. The proposed method, enhanced with a low‐pass filter and compared to Skogestad internal model control, demonstrates superior performance in industrial applications, offering quick set‐point tracking, effective load disturbance rejection, and smooth control signals. Future research directions include experimental validation and robustness analysis under varying system parameters.

This study introduces some remarks on generalized fractional integral and differential operators, which generalize some familiar fractional integral and derivative operators, with respect to a given function. We briefly explain how to formulate representations of generalized fractional operators. Then, mainly, we propose a predictor–corrector algorithm for the numerical simulation of initial value problems involving generalized Caputo-type fractional derivatives with respect to another function. Numerical solutions of some generalized Caputo-type fractional derivative models have been introduced to demonstrate the applicability and efficiency of the presented algorithm. The proposed algorithm is expected to be widely used and utilized in the field of simulating fractional-order models.

This paper addresses the oscillatory properties of a class of second-order neutral delay differential equations (NDDEs) and introduces a numerical scheme based on a fourth-order predictor-corrector multistep method for solving NDDEs of this type. An example in the family of oscillatory equations has been integrated by using the proposed numerical scheme. Results confirm the theoretical assumptions.

The aim of this article is to develop a modified predictor–corrector scheme for solving the system of nonlinear -Caputo fractional differential equations with order . By using the graded mesh and considering the predictor–corrector scheme for -Caputo fractional derivative, the numerical solutions of nonlinear -Caputo fractional-order systems are derived. Moreover, the error estimations of predictor–corrector scheme with graded mesh are also investigated. Particularly, the accuracy of numerical solutions depended on the function and the partition size on graded mesh. Numerical examples for linear and nonlinear fractional differential systems with various kernels and meshes are considered to explain the value and effectiveness of the proposed schemes.

As teachers returned to the classroom for the 2020-2021 school year, they faced new and challenging environments, instructional approaches, and roles as educators. The current study is one of the first empirical studies that identified factors contributing to teacher burnout due to COVID-19 (coronavirus disease) and instruction during fall 2020. Controlling for demographics, the results found significant predictors for teacher burnout-stress those being COVID-19 anxiety, current teaching anxiety, anxiety communicating with parents, and administrative support. The results are important for schools and researchers to consider when it comes to the impact of COVID-19 on teachers.

Background/Objectives: To evaluate the prognostic value of easily obtainable biomarkers for patients undergoing percutaneous microwave ablation (MWA) for colorectal liver metastases (CLMs). Prior studies showed that simple biomarkers, such as the lymphocyte-to-monocyte ratio (LMR), albumin-to-globulin ratio (AGR), platelet-to-lymphocyte ratio (PLR), and neutrophil-to-lymphocyte ratio (NLR), as well as cancer-specific markers, like carcinoembryonic antigen (CEA), might have a prognostic role in various malignancies; however, none of these were assessed in patients undergoing MWA for CLMs. Methods: Based on the simple laboratory results, which were determined prior to the ablation, several biomarkers, including the LMR, AGR, PLR, and NLR, were calculated. The log-rank test’s optimal cutoff points for continuous variables were determined. Subsequently, univariable and multivariable Cox regression models were utilized to determine the association between various features and overall survival (OS). Results: This study included 57 CLM patients with a mean age of 63 ± 12.5 years at the time of ablation with a mean follow up of 30.9 months. The univariable model demonstrated that a high level of CEA (cutoff: 29.1 ng/mL; HR: 3.70) and a high LMR (cutoff: 5.32; HR: 4.05) were related to worse OS, whereas a high NLR (cutoff: 2.05; HR: 0.31) and primary left-sided colon cancer (HR: 0.36) were positive prognostic factors. The multivariable regression model confirmed these findings, with the exception of the LMR, which was no longer significantly associated with OS. Conclusions: This study demonstrates the feasibility of overall survival prediction and thus patient stratification based on easily obtainable biomarkers and clinicopathological features in CLM patients undergoing MWA.