This paper develops a dynamical systems model of an economy with recursively self-improving artificial intelligence and financialization. The model features quadratic self-amplification in both AI capability ($\lambda A^2$) and financial capital ($\gamma_F K_f^2$), coupled through investment flows. It is shown that under mild conditions, the system exhibits a finite-time singularity where AI capability, AI capital, and financial capital diverge. Near the singularity, the wealth ratio between capital owners and workers diverges super-exponentially, with financialization amplifying the exponent by a factor $\gamma_F/\eta$. Introducing taxes on AI returns ($\tau_{ai}$) and financial gains ($\ta... More >

This paper explores heat transfer and MHD flow of different shapes of (Ag-TiO$_{2}$/PAO Oil) hybrid nanoparticles through an unsteady radially stretching sheet consider variable thermal conductivity and viscosity. The present investigation explores the thermal radiation impact of different shapes (platelet, sphere, brick, blade, cylinder) of hybrid nanoparticles with variable viscosity($\mu_\mathrm{hnf}$) and thermal conductivity($k_\mathrm{hnf}$) under the suction and partial slip parameter. This study presents a novel analysis of variable thermal conductivity and viscosity for different shapes of hybrid nanoparticles. The nonlinear ODEs are generated by proper transformation from governing... More >

A unified fractional simplest equation framework is developed for nonlinear power-law wave equations whose travelling-wave reductions lead to $U'' + \lambda U^p = 0$, $p>1$. In contrast to classical simplest equation methods restricted to integer polynomial expansions, we introduce a fractional power ansatz $U(\xi)=A\phi^\alpha(\xi)$ derived from a dominant balance principle. A general scaling theorem is established, proving that the admissible travelling-wave exponents are uniquely determined by $\alpha(p-1)=2$, yielding the explicit fractional law $\alpha=\frac{2}{p-1}$. Consequently, the equation admits algebraic travelling waves of the universal form $U(\xi)=A(\mu\xi+C_0)^{-2/(p-1)}$, wi... More >

The study of coupled reaction transport in Casson rheology bridges the gap between idealized Newtonian models and practical non-Newtonian fluids, as chemically reacting nanoparticles alter the concentration and thermal behavior of the base fluid. This complexity intensifies when nanoparticles are introduced into conventional refrigerants. This work presents a unified investigation of radiative and viscous dissipative magnetohydrodynamic flow of a chemically reacting Casson nanofluid over an inclined slippery stretching surface embedded in a non-Darcy porous medium. The simultaneous consideration of Casson rheology, nanoparticle-enhanced heat transfer, magnetic control, surface slip, chemical... More >

Entropy optimization in the dissipative flow of a viscous liquid with a chemical species of quartic autocatalysis inside wedge geometry is investigated in this study by executing the revised Buongiorno model using numerical simulations. To demonstrate the feasibility of this approach, an illustration of the well-known model of laminar flow in the wedge domain of a planar surface is provided. The term for nanoparticles amalgamation in the heat equation is omitted, which accounts for additional involvement brought on by the migration of the nanoparticles in relation to the fluid. In addition, the energy released by autocatalysis processes is assumed to be insignificant. The studied nanofluid a... More >

This study presents a mathematical and computational analysis of blood flow in the abdominal aorta under healthy, aneurysmal, and rupture-related conditions. The proposed framework combines a Newtonian fluid approximation with a Lattice Boltzmann formulation to simulate the hemodynamic behavior of the aorta in three-dimensional geometry. The governing equations were implemented in Python, allowing the generation of numerical simulations and corresponding three-dimensional visualizations of aneurysm progression. The analysis considered clinically inspired stages ranging from the healthy vessel to advanced aneurysmal dilation and rupture. The results showed that aneurysm growth significantly a... More >

Linguistic picture fuzzy soft sets (LPFSSs) provide a powerful tool for handling uncertainties in decision-making problems, particularly when multiple parameters are involved. By integrating the advantages of linguistic picture fuzzy sets (LPFSs) and soft sets (SSs), LPFSSs prove especially effective in situations involving imprecise and ambiguous information. This study extends the conventional CRITIC (Criteria Importance Through Inter-criteria Correlation) and EDAS (Evaluation based on Distance from Average Solution) methods to the LPFSS environment. First, the definitions of LPFSSs and linguistic picture fuzzy soft numbers (LPFSNs) are introduced along with their key properties. Subsequen... More >

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 >