Heart disease is a significant global health issue, contributing to high morbidity and mortality rates. Early and accurate heart disease prediction is crucial for effectively preventing and managing the condition. However, this remains a challenging task to achieve. This study proposes a machine learning model that leverages various preprocessing steps, hyperparameter optimization techniques, and ensemble learning algorithms to predict heart disease. To evaluate the performance of our model, we merged three datasets from Kaggle that have similar features, creating a comprehensive dataset for analysis. By employing the extra tree classifier, normalizing the data, utilizing grid search cross-validation (CV) for hyperparameter optimization, and splitting the dataset with an 80:20 ratio for training and testing, our proposed approach achieved an impressive accuracy of 98.15%. These findings demonstrated the potential of our model for accurately predicting the presence or absence of heart disease. Such accurate predictions could significantly aid in early prevention, detection, and treatment, ultimately reducing the mortality and morbidity associated with heart disease.

Present contribution is concerned with the construction and application of a numerical method for the fluid flow problem over a linearly stretching surface with the modification of standard Gradient descent Algorithm to solve the resulted difference equation. The flow problem is constructed using continuity, and Navier Stoke equations and these PDEs are further converted into boundary value problem by applying suitable similarity transformations. A central finite difference method is proposed that gives third-order accuracy using three grid points. The stability conditions of the present proposed method using a Gauss-Seidel iterative procedure is found using VonNeumann stability criteria and order of the finite difference method is proved by applying the Taylor series on the discretised equation. The comparison of the presently modified optimisation algorithm with the Gauss-Seidel iterative method and standard Newton’s method in optimisation is also made. It can be concluded that the presently modified optimisation Algorithm takes a few iterations to converge with a small value of the parameter contained in it compared with the standard descent algorithm that may take millions of iterations to converge. The present modification of the steepest descent method converges faster than Gauss-Seidel method and standard steepest descent method, and it may also overcome the deficiency of singular hessian arise in Newton’s method for some of the cases that may arise in optimisation problem(s).

Prishchepov [16] proved that all equations of length at most six over torsion-free groups are solvable. A different proof was given by Ivanov and Klyachko in [12]. This supports the conjecture stated by Levin [15] that any equation over a torsion-free group is solvable. Here it is shown that all equations of length seven over torsion-free groups are solvable.

The recent study was concerned with employing the finite element method for heat and mass transfer of MHD Maxwell nanofluid flow over the stretching sheet under the effects of radiations and chemical reactions. Moreover, the effects of viscous dissipation and porous plate were considered. The mathematical model of the flow was described in the form of a set of partial differential equations (PDEs). Further, these PDEs were transformed into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. Rather than analytical integrations, numerical integration was used to compute integrals obtained by applying the finite element method. The mesh-free analysis and comparison of the finite element method with the finite difference method are also provided to justify the calculated results. The effect of different parameters on velocity, temperature and concentration profile is shown in graphs, and numerical values for physical quantities of interest are also given in a tabular form. In addition, simulations were carried out by employing software that applies the finite element method for solving PDEs. The calculated results are also portrayed in graphs with varying sheet velocities. The results show that the second-order finite difference method is more accurate than the finite element method with linear interpolation polynomial. However, the finite element method requires less number of iterations than the finite difference method in a considered particular case. We had high hopes that this work would act as a roadmap for future researchers entrusted with resolving outstanding challenges in the realm of enclosures utilized in industry and engineering.

Let G be a nontrivial torsion-free group and has a solution over G provided a single relation on coefficients of s(t) holds. We also generalize our results to equations containing higher powers of t. The later equations are also related to Kaplansky zero-divisor conjecture.

A modified class of temporal discretization schemes for partial differential equations (PDEs) is proposed, explicit and second to fifth-order accurate in time. In time, the stability region of the proposed modified second-order scheme is larger than the standard second-order Adams–Bashforth method constructed on two time levels. A modification made for the Du Fort–Frankel method was also implemented in the proposed second-order scheme, which permits the little larger stability region, but the scheme becomes first-order accurate. Since the Du Fort–Frankel method cannot be employed without a modification of averaging in time levels, the proposed second-order scheme can be used without any modification. The proposed modified scheme with different orders in space and second orders in time was implemented for heat and mass transfer of chemically reactive fluid flow in a rectangular duct. The flow is generated due to applying different pressure gradients. The contour plots of velocity, temperature, and concentration profiles are portrayed at different pressure gradients; Péclet number in heat transfer, Péclet number in mass transfer, reaction parameter, and at different times. In addition, stability and convergence conditions for the considered system of linear and non-linear PDEs consisting of non-dimensional momentum, energy, and concentration equations were found for two cases. The displayed graphs depict the transfer of heat in the fluid, which rises due to heated boundaries, and the transfer of mass in the fluid at various moments. Classical models can be solved using the proposed method, which has a faster convergence rate than the standard or classical approach. This approach is illustrated through computer simulations that demonstrate its key computational features. It is believed that the data presented in this study will serve as a useful source for future fluid flow investigations to be conducted in an industrial setting within an enclosed area.