Vol. 12, No. 06 [June 2026]

The mathematical tumor model is an efficient tool for analyzing the tumor growth and propagation. It also helps to plan the treatment in a more accurate way. The net killing rate of tumor cells helps to monitor the growth or decay of the tumor. In this article, two types of one-dimensional time-fractional tumor model is taken based on two types of net killing rate. In addition, fuzzy initial condition is considered. The solution is obtained by the use of an analytical method called the optimal homotopy asymptotic laplace transform method (OHALTM). Numerical experiments are given for both cases to validate the new approach. The small margin of absolute errors shows the accuracy of the solutions. The fractional derivative with fuzzy initial conditions in the tumor model is also discussed.
Keywords: Tumor model, Fractional differential equations, Optimal homotopy asymptotic laplace transform method, Fuzzy initial condition.

Transition-metal carbide/nitride multilayer coatings have attracted significant interest due to their excellent combination of hardness, wear resistance, thermal stability, and chemical durability. In this study, multilayer coatings were synthesized using an energetic thin-film deposition technique and subsequently characterized to evaluate their structural, mechanical, and tribological properties. The multilayer architecture promoted the formation of dense nanocrystalline structures with strong interfacial bonding between adjacent layers. The coatings exhibited enhanced mechanical performance compared with conventional single-layer counterparts, owing to the combined effects of interface strengthening and grain refinement. Furthermore, the multilayer configuration contributed to improved wear resistance and reduced friction during sliding contact. The results demonstrate that carbide/nitride multilayers are promising candidates for advanced protective coating applications requiring high mechanical reliability and long-term durability.
Keywords:Angular color uniformity, Color quality scale, Correlated color temperature, Light scattering, White LEDs, ZrC phosphor.

The rapid global scaling of digital payment ecosystems has created an infrastructure challenge that conventional capacity planning approaches cannot adequately address: transaction volumes in 2025 exceed $24 trillion globally and continue to expand at a compound annual growth rate of 8.44%, while intraday load variance in payment processing systems regularly reaches 10 to 15 times baseline levels during peak hours. This study investigates how advanced load forecasting techniques, combined with adaptive capacity planning frameworks, can be systematically applied to support mass-market digital payment deployments. Through a comparative analysis of forecasting methods including ARIMA, gradient boosting, univariate and multivariate long short-term memory networks, and a proposed hybrid ensemble model, and through examination of operational case studies from UPI, Stripe, WeChat Pay, and a central bank digital currency pilot, the research demonstrates that hybrid ensemble forecasting achieves a mean absolute percentage error of 2.6% compared to 8.4% for classical ARIMA models, reduces mean time to scale-out from 48 seconds to 17 seconds, and lowers infrastructure overprovisioning rates from 52% to 14%. The study proposes an original three-layer adaptive capacity architecture integrating predictive autoscaling, observability-driven feedback, and cost-constrained optimization. The findings are of primary relevance to engineering teams, fintech product architects, and infrastructure planners responsible for payment platform reliability and cost governance.
Keywords:digital payments, load forecasting, adaptive capacity planning, LSTM, autoscaling, microservices, CBDC, observability, Kubernetes, AIOps.