Green finance is increasingly viewed as a critical mechanism for accelerating environmental recovery and sustainable development, yet existing research tends to focus on outcomes rather than drivers. We examine firm-level determinants of green finance in Saudi manufacturing firms during 2010-2021, focusing on energy market competitiveness, environmental regulation, and green innovation. The analysis uses panel data from 35 firms and methods including partial least squares, GMM, fixed effects, and random effects to ensure robustness. Our results show that stricter environmental regulation and greater market competitiveness significantly enhance green finance performance. Crucially, product-oriented green innovations lead to quicker adoption of green finance than advanced eco-innovations, likely because they offer faster financial returns. By identifying these policy and market drivers in an oil-dependent economy, the study provides actionable guidance for regulators and managers to calibrate environmental rules, strengthen competitive conditions, and accelerate investment in cleaner production and sustainable finance, supporting Saudi Arabia's sustainable development goals.
Lead telluride (PbTe) is a well-known thermoelectric material with a figure of merit (zT) typically exceeding 1 at intermediate temperatures. However, due to its intermetallic properties, the oxidation of PbTe introduces oxygen-related defects. These defects not only destabilize the crystal but also reshape the delicate balance between electrical and thermal conductivity. The present work investigates the influence of Ag incorporation on its thermoelectric transport and oxidation behavior. Unconventional p-type silver-doped PbTe (PbTe1-xAgx, where x = 0, 0.04, 0.08, 0.12) was synthesized. Structural analysis confirmed the successful incorporation of Ag into the lattice. Density functional theory (DFT) calculations revealed that Ag doping induces a narrow bandgap semiconducting to semi-metallic transition, which potentially enhanced the electrical conductivity. Concurrently, phonon calculations indicated intensified phonon scattering, which contributes to a suppressed lattice thermal conductivity. This synergistic effect of electronic band engineering and phonon suppression proved as a highly effective strategy for enhancing thermoelectric performance. As a result, the thermoelectric figure of merit, zT, improved from 1.06 for pristine PbTe to 1.37 at 753 K for the PbTe0.88Ag0.12 composition, representing a 29.2% enhancement. Beyond improving the performance, Ag doping also significantly enhanced the material's operational stability. Comprehensive thermal and structural analyses, supported by time- and temperature-dependent oxidation studies, demonstrated that Ag doping leads to a markedly reduced oxidation rate. This suppression of oxidation effectively stabilizes the material against degradation at both room temperature and intermediate operating temperatures.
In liquid chromatography simultaneous gradients of solute and temperature can be applied to control adsorption of solute on the stationary phase by simultaneously changing the composition of the mobile phase and the temperature. These parallel variations alter adsorption equilibria and solute migration rates. The work extends a general rate model to incorporate such parallel gradients, enabling the simulation of two-mode gradient elution. The model consists of coupled nonlinear convection-diffusion equations which describe the simultaneous transport of mass, energy, and solvent composition within a chromatographic column. By introducing time-dependent gradients of temperature and solvent composition, it accurately represents advanced elution protocols. The integrated retention model combines the theory of linear solvent strengths with modified van't Hoff behavior, defining Henry's constants and the non-linearity coefficients as functions of solvent composition and temperature. The governing equations are solved with a high-resolution finite-volume scheme, effectively capturing temperature-dependent retention, nonlinear adsorption, and sharp concentration fronts. The effects of positive, negative, and mixed solvent-temperature gradients, as well as important operational parameters, on peak shape and separation efficiency are quantified through numerical simulations. The findings show that, in comparison to single-gradient or isothermal operations, combined gradients achieve faster elution, better peak symmetry, and better separation performance.
This study introduces an efficient and accurate two-stage explicit computational scheme for solving partial differential equations (PDEs) containing first-order time derivatives. The suggested method is a modification of the classical Runge-Kutta scheme that introduces a new first-stage formulation. This minimizes numerical error with moderate step sizes while preserving the stability region of the classical method. Spatial discretization is performed using a sixth-order compact finite-difference scheme to obtain high-resolution solutions. The analysis of stability and convergence is strictly determined for both scalar and system forms of convection-diffusion-type equations. To illustrate the suitability of the method, a dimensionless mathematical model of the unsteady, incompressible, laminar flow of a Prandtl-type non-Newtonian nanofluid over a Riga plate is considered, accounting for viscous dissipation, thermophoresis, Brownian motion, and a magnetic field. Here, the Prandtl ternary nanofluid is defined as a non-Newtonian nanofluid that follows the Prandtl rheological model, and it exhibits three critical transport phenomena: heat conduction, viscous dissipation, and nanoparticle diffusion. Representative values of the Prandtl number Pr=3 and Reynolds number Re=5 are used to perform the simulation, and other parameters, including but not limited to the Hartmann number Ha, Williamson number We, thermophoresis Nt and Brownian motion Nb, are varied to evaluate the flow behavior. Moreover, an artificial neural network (ANN)-developed surrogate model is used to calculate the skin friction coefficient and the local Sherwood number, using five input parameters: the Reynolds number, Prandtl number, Schmidt number, Brownian motion parameter, and thermophoresis parameter. The governing partial differential equations yield high-fidelity numerical data used to train the surrogate model. The data is split into 80% for training, 10% for validation, and 10% for testing. The ANN is tested using regression analysis and error histograms, which demonstrate high accuracy and generalization capacity. Numerical simulation combined with AI-based prediction is a cost-efficient method for real-time estimation of complex non-Newtonian nanofluid systems.
This study derives novel exact traveling wave solutions for the nonlinear (1+1)-dimensional Chafee-Infante equation by synthesizing the generalized first integral method (GFIM) with Laurent polynomial expansions. As a fundamental reaction-diffusion model, the Chafee-Infante equation governs pattern formation in diverse systems-from biological to chemical and physical contexts- yet its strong nonlinearity poses persistent challenges to classical integration techniques such as the inverse scattering transform or Hirota's method. We transform the equation into an autonomous polynomial system and employ the division theorem to systematically identify its first integrals, thereby circumventing the need for auxiliary equations or ansatz-based heuristics. By introducing Laurent polynomial ansatzes of varying complexity-ranging from first-degree to higher-order expansions- we yield compact rational-exponential solutions that are both exact and computationally tractable. The validity of these solutions is confirmed through symbolic computation in Mathematica, while a detailed graphical analysis elucidates their behavior-from bounded, dissipative profiles to singular structures-across different parameter regimes, including the critical thresholds C = 0 and C = 2 where blow-up phenomena emerge. This work underscores the efficacy of merging Laurent series with algebraic methods, offering a powerful and generalized tool for extracting exact solutions from a broader class of intractable nonlinear partial differential equations (PDEs) arising in mathematical physics and applied mathematics.
