International Journal of Mathematics and Mathematical Sciences

In the contemporary world, the effect of faith in religion cannot be underestimated or overemphasized. In the olden days, traditional religion/faith of a particular locality was the only practice obtainable; however, new faiths emerged and are being absorbed in recent times. Extremism in the newly absorbed faith began to cause the indigenous religion to collapse and increase violence against innocent ones. This paper investigated the interaction between the extremism of faith leading to the act of terror and a susceptible individual (members of the society) to guide the policymakers and decision implementers to embrace the proposed model for counterterrorism for effective management of the insurgency. Mathematical modelling of epidemiology was conceptualized for the model formulation, and the resulting autonomous differential equations were critically analyzed with the Lipschitz condition, next generation matrix, and Bellman and Cooke’s criteria for the management of insurgency in the society. Thresholds were obtained to curtail recruitment into the fanatical groups, and the results of the simulated proposed model identified critical factors (parameters) to be considered for the complete eradication of violence in human society.

A one-dimensional nonstationary nonlinear moment system of equations and an approximation of Maxwell’s microscopic boundary condition will be introduced. The flight speed and surface temperature of the aircraft are included in the moment system of equations as coefficients. Macroscopic boundary conditions also depend on the surface temperature of the aircraft. The quantity of macroscopic boundary conditions for the moment system of equations depends on the parity of the approximation number of the moment system of equations. We state the initial and boundary value problem for the moment system of equations in the third approximation under macroscopic boundary conditions. This paper proves the existence and uniqueness of the solution of the abovementioned problem in the space of functions continuous in time and summable in the square by spatial variable. The theorem on the existence and uniqueness of a solution of the initial and boundary value problem for the moment system of equations in the third approximation is proved by the method of a priori estimation and using the Galerkin method and Tartar’s compensated compactness method.

The aim of this paper is to establish the prime filter theorem for multilattices.

One of the more restrictive methods of improvement is the augmented Lagrange method. Two versions are built in the external framework and the internal framework of the proposed method. The first basic version of the proposed algorithm includes a new derivation of Lagrange multiples and different penalty criteria, and the second version is the internal framework in which the unconstrained algorithm known as the conjugate gradient (CG) method was incorporated; also, a new parameter was derived in the search direction. The numerical results are indicative of the stability, efficiency, and speed of the proposed algorithm, based on performance profiles provided by Dolan and More.

In this research, the normalization performance of the proposed adjusted min-max methods was compared to the normalization performance of statistical column, decimal scaling, adjusted decimal scaling, and min-max methods, in terms of accuracy and mean square error of the final classification outcomes. The evaluation process employed an artificial neural network classification on a large variety of widely used datasets. The best method was min-max normalization, providing 84.0187% average ranking of accuracy and 0.1097 average ranking of mean square error across all six datasets. However, the proposed adjusted-2 min-max normalization achieved a higher accuracy and a lower mean square error than min-max normalization on each of the following datasets: white wine quality, Pima Indians diabetes, vertical column, and Indian liver disease datasets. For example, the proposed adjusted-2 min-max normalization on white wine quality dataset achieved 100% accuracy and 0.00000282 mean square error. To conclude, for some classification applications on one of these specific datasets, the proposed adjusted-2 min-max normalization should be used over the other tested normalization methods because it performed better.

In this work, we show how to estimate stress strength (SS) reliability when the stress (Y) and strength (X) distributions are generalized exponentials with a common scale parameter. The SS reliability estimator is considered in view of neoteric ranked set sampling (NRSS) and median ranked set sampling (MRRS). We acquire an estimate of the reliability (R) when such samples of the stress and strength random variables are gathered using the same NRSS technique. Furthermore, the reliability estimator is derived when the stress distribution data are in the pattern of MRSS with just an odd/even set size and the strength distribution data are derived from NRSS and vice versa. The simulation results are used to evaluate and understand the adequacy of a variety of estimators for the suggested schemes. Based on our simulated results, we found that NRSS-based stress strength reliability estimates are more efficient than MRSS-based stress strength reliability estimates. The analysis of real-world data is used to implement the recommended estimators.