National Institute of Technology, Manipur

This manuscript studies the Bose-Einstein condensate (BEC) stars in the light of f(R,T) gravity here with Durgapal-Fuloria (DP) metric ansatz. The function under this study features as f (R, T) = R + 2riT, where ri represents the coupling constant. With the help of it, we have formulated a stellar model describing the isotropic matter here within. Our analysis covers energy conditions, equation of state (EoS) parameter and gradients of the energy-momentum tensor components for a valid BEC stellar framework within f (R, T) gravitational theory with satisfactory results. The model's stability has been validated via multiple stability criteria viz., the velocity of sound, study of adiabatic index and surface redshift where all are found to be lying within the acceptable range for our stellar model. Thus in all the cases we have found our model to be stable and realistic. From the graphical representations the impact of the coupling constant and the parameter of the DP metric potential are clearly visible. Thus we can state that with all the above-mentioned features we have introduced new stellar solutions for BEC stars with enhanced precise results in this modified gravity.

We propose an efficient iterative method called Picard-CR for approximating fixed points under weak perturbative contraction conditions in uniformly convex hyperbolic metric spaces. Theoretical analysis establishes both weak and strong convergence, with performance validated against classical methods (CR, Picard-Noor, and Picard-SP) through numerical experiments. We extend our convergence results to non-expansive and contraction mappings, supported by MATLAB-based visualizations. The iterative scheme is shown to be stable and more efficient, with direct application to computing equilibrium concentrations in reversible chemical reactions. Our findings contribute not only to fixed point theory but also provide practical computational tools for chemical and engineering problems.

Two-dimensional (2D) nitride MXenes are promising candidates for energy storage, corrosion protection, and optoelectronics, but their practical use is limited by layer restacking, structural instability, and insufficient active sites. Herein, we report the synthesis of binder-free Fe-decorated Ti2NTx MXene heterostructures via fluoride salt etching followed by in situ chemical reduction. Fe incorporation introduces redox-active centres (Fe2+/Fe3+, Fe/Fe2+), stabilises the MXene surface through Fe-Ti and Fe-N bonding, and alters the defect-state distribution responsible for excitation-dependent photoluminescence (PL). The optical band gap narrowed from 4.78 eV in Ti2AlN MAX to 3.7 eV in Ti2NTx MXene and was further tuned from 3.57 to 5.35 eV in Fe@Ti2NTx heterostructures. PL analysis confirmed the presence of shallow defect states (blue emission similar to 470 nm) and deep-level defects (green/yellow emission similar to 530-580 nm), with Fe decoration suppressing Al-related traps and stabilizing defect distributions across excitation wavelengths. X-ray photoelectron spectroscopy (XPS) deconvolution further confirmed the coexistence of Ti-N, Ti-O, Fe-Ti, Fe-Fe, and Fe-N bonding configurations, highlighting strong electronic interactions between Fe and the Ti2NTx host. The optimized 1 mM Fe@Ti2NTx electrode delivered a specific capacitance of 124.53 F/g at 1 A g(-1) and 57.08 F/g at 0.005 V/s, with 97.25 % retention after 10,000 cycles. Corrosion current was reduced to 0.28 mu A with a suppressed corrosion rate of 1.49 x 10(-9) mm y(-1) in 1 M H2SO4. These results establish Fe@Ti2NTx MXene as a multifunctional heterostructure with enhanced charge storage, durability, and defect-engineered optoelectronic response.

This study reveals a significant advancement in alpha-Fe2O3 modified with ZnO through high-temperature argon plasma treatment, uncovering an unprecedented intense single magnon scattering peak at similar to 800 cm(-1) by Raman Spectroscopy. Sophisticated crystallographic and microscopic analysis expose a complex heterophase interface comprising ZnO, alpha-Fe2O3 and cubic iron oxides. However, the magnon peak was not observed in the fractionally reduced alpha-Fe2O3 to cubic iron oxides system. Further, this magnon signal diminished progressively and ultimately vanished over a three-year observation period. The experimentally observed Raman mode demonstrates remarkable agreement with the theoretical predictions derived from the simple Ising model, substantiating the underlying magnetic interaction.

In this work, the effects of viscosity in gravity are investigated by considering the model with an new exponential bulk viscosity of the form . The Hubble parameter is derived in terms of redshift and constrain the model parameters using observational datasets, including CC, DESI DR2 BAO and Pantheon+ datasets, via the MCMC approach. The best‐fit values of the parameters are obtained and the evolution of cosmological parameters is analyzed. The results indicate a transition from a decelerated to an accelerated expansion phase, with the present deceleration parameter value for the joint dataset. The equation of state parameter approaches at late times and the SEC is violated, supporting cosmic acceleration. The statefinder analysis shows that the model evolves from a Chaplygin gas phase to quintessence and finally converges to . Additionally, the impact of viscosity is examined, showing that its influence is significant in the early Universe but diminishes over time. These findings suggest that viscosity plays a crucial role in cosmic evolution within gravity, providing a viable alternative framework for late‐time acceleration.