This study conducts a comparative evaluation of seven numerical methods for finding roots of nonlinear equations: Bisection, Regula-Falsi, Fixed-Point Iteration, Newton-Raphson, Secant, Aitken's \(\Delta^2\), and Steffensen. The aim is to analyze the effectiveness of each method based on convergence speed, numerical accuracy, stability, and computational time efficiency. Algorithm implementation was carried out in the Python programming language using NumPy, SymPy, Pandas, and Matplotlib libraries. Test functions included polynomial, trigonometric, exponential, and mixed functions to represent diverse functional characteristics. The results indicate that Steffensen and Newton-Raphson achieve... More >

In this paper, some sufficient conditions for the reverse-order law of the weak core inverse are obtained. Several characterizations of the reverse-order law for this generalized inverse are then established. In addition, some results concerning the absorption law for the weak core inverse are proved. More >

Momentum-based investment strategies face persistent challenges from noise contamination in financial time series, particularly within emerging markets such as China's ChiNext board. Traditional enhancement approaches typically address symptoms rather than underlying causes, resulting in continued vulnerability to market regime changes and performance deterioration. This study develops and evaluates a dual-denoising framework that integrates wavelet analysis for temporal noise reduction with isolation forest algorithms for cross-sectional anomaly detection. Our methodology employs comprehensive analysis of 1,200-1,300 ChiNext stocks spanning the 2015-2025 period, utilizing multiple machine l... More >

This work investigates the formation and dynamics of electrostatic freak waves in pair-ion (PI) and pair-ion--electron (PIE) plasmas. The analysis begins with the derivation of the Korteweg--de Vries (KdV) equations for both plasma configurations, from which the corresponding nonlinear and dispersive coefficients are obtained. By employing the wave superposition principle, the KdV equations are systematically reduced to the nonlinear Schrödinger equation (NLSE), enabling the exploration of modulation instability and rogue wave generation. Analytical solutions of the NLSE are utilized to construct parametric plots that elucidate the evolution of freak waves in PI and PIE plasmas. Comparative... More >

This study investigates the magnetohydrodynamic (MHD) flow of Boger tri-hybrid nanofluid (tri-HNF) through a stretching disk. A novel machine learning technique, specifically the Levenberg--Marquardt (LM) scheme under a backpropagated artificial neural network (ANN), is used to predict the flow dynamics with heat and mass transfer. The Cattaneo-Christov mass and heat fluxes model, permeable media, and viscous dissipation are considered. The well-known Brinkman-Hamilton and Crosser model is used to describe thermal conductivity and viscosity models. The computational solution to the current problem has been obtained using the Bvp4c approach, which is based on finite differences. In order to e... More >