In this paper, we present a modified three-point superclass of Block Backward Differentiation Formula (BBDF) for the efficient numerical solution of stiff systems of ordinary differential equations (ODEs). The principal enhancement of this work is a structural modification of the classical BBDF that forms a new parameterized superclass of methods, leading to improved stability and reduced error constants compared with the standard three-point BBDFs. The proposed scheme is formulated as a fully implicit block method capable of simultaneously producing three solution approximations within each integration step. A detailed theoretical analysis is conducted to establish the order of accuracy, co... More >

This paper proposes a dynamic programming (DP) approach for a stochastic multi-period allocation problem, whereby fleet of vehicles are assigned from stations to destinations with multiple alternative routes in order to maximize returns, while the vehicles are subject to random failure. In the process of managing the business, the company is assumed to incur proportional management costs and pay tax to government. The expected returns is modelled as a function of random failure of vehicles due to bad roads and depreciation. The depreciation rate is assumed to follow a straight-line approach. The breakdown rate is modelled as function of the rate of bad roads on the fleets, depreciation rate... More >

In order to improve heat transfer efficiency, it is essential to examine that MHD hybrid nanofluid flows behave under convective and slip boundary conditions. Researchers have looked at a variety of factors when adding hybrid nanofluids to these flows, including Forchheimer number, radiation, magnetic fields, Biot number, and the Joule heating. The novelty of the current study lies in investigating the consequences of Casson fluid in the Darcy Forchheimer flow of a three-dimensional rotating hybrid nanofluid, which have not been thoroughly covered in the literature. This includes combinations of heat sources/sinks, magnetic parameters, and radiation absorption as well as convective condition... More >

A nonlinear compartmental model is developed to analyze crime dynamics in a structured society. The population is stratified into eight compartments: \(S(t)\) (susceptible), \(E(t)\) (exposed), \(C(t)\) (active criminals), \(C_v(t)\) (convicted criminals), \(P_h(t)\) (passive-honest), \(P_c(t)\) (committed-honest), \(J_h(t)\) (honest judges), and \(J_c(t)\) (corrupt judges). The model incorporates nonlinear mechanisms such as institutional corruption (\(\kappa_1\)), judicial correction (\(\kappa_2\)), recidivism feedback (\(\rho_1,\rho_2\)), exposure intensity (\(\eta_1\)), and rehabilitation (\(r_2\)), providing a realistic portrayal of crime--justice interactions. Solutions remain positive... More >

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 >