In this paper, we study the asymptotic behavior of energy and action ground states to the following pseudo-relativistic Hartree equation (root/-c(2) Delta + m(2)c(4) - mc(2)) u + lambda u = (|x|(-1) * |u|(2)) u as the speed of light c - infinity. We obtain an asymptotic expansion of the ground state as c -> infinity, which is new in the case of the energy ground state and generalizes the results of Choi, Hong, and Seok [3] for the action ground state. (c) 2026 The Author(s). Published by Elsevier Inc.
The Doyle–Kirmse reaction provides direct access to chiral allylic sulfides through sulfur-ylide formation and subsequent [2,3]-sigmatropic rearrangement, although asymmetric control remains challenging. This study reports the engineering of Vitreoscilla hemoglobin (VHb) into a stereoselective biocatalyst for the Doyle-Kirmse reaction, utilizing an integrated strategy that combines computer-aided design, semi-rational protein engineering, and directed evolution. Through this approach, we successfully developed a VHb variant, VHbVF (Y29V/L57F), which serves as a highly efficient and enantioselective catalyst. Under mild conditions (PBS buffer, pH 7.4, 25 °C), the VHbVF-catalyzed model reaction achieved a yield of 98% with an enantiomeric excess (ee) of up to 85%. The biocatalytic system also exhibited a broad substrate scope, accommodating a variety of substituted allyl phenyl thioethers and diazo esters, demonstrating good functional group tolerance and stereoselectivity (up to 85% ee). This work provides the first example of employing engineered VHb for asymmetric Doyle–Kirmse reactions, expanding the catalytic repertoire of hemoproteins in non-natural carbene-transfer chemistry and offering an alternative biocatalytic approach to chiral sulfur-containing compounds.
Intelligent optimization remains a critical challenge in modern engineering design and planning, primarily due to the multimodal, non-linear, and tightly constrained nature of real-world decision spaces. In such environments, balancing global exploration with local exploitation to avoid premature convergence is a well-known difficulty. This study proposes the Elite-Inspired Sociocultural Algorithm (EISA), an optimization approach inspired by sociocultural mechanisms in human societies. EISA integrates intra-group collaboration, inter-group cooperation, and a dual-phase inter-group competition mechanism within a hierarchical structure to maintain a dynamic search balance. The proposed method is evaluated using 23 classical test functions alongside the CEC2019, CEC2020, and CEC2022 benchmark suites. Quantitatively, EISA achieved a leading average Friedman rank (2.22) across the classical functions, demonstrating competitive accuracy and robustness compared to nine advanced algorithms. Furthermore, its practical effectiveness is verified through four real-world engineering design cases and a three-dimensional unmanned aerial vehicle (UAV) path planning problem. Under complex and constrained UAV scenarios, EISA consistently generated feasible safe paths and achieved lower comprehensive path costs (e.g., 5.28 & times; 103) than the evaluated comparative planners. These results indicate that EISA serves as a reliable and efficient intelligent optimization framework for tackling challenging engineering applications.
The hydrazine oxidation reaction (HzOR) has emerged as a kinetically superior substitute for the oxygen evolution reaction (OER) in energy-efficient hydrogen (H2 ) generation. However, engineering bifunctional catalysts that retain high activity for both H2 evolution reaction (HER) and HzOR under high-currentdensity operation continues to pose a substantial hurdle. Herein, an effective Pt-doping strategy serves as an effective means to manipulate its d-band center, inducing favorable electronic modifications that optimize intermediate binding and simultaneously reduce activation barriers for HER and HzOR. Therefore, the representative 10 %Pt-RuO2 nanofibers (NFs) exhibit remarkable catalytic metrics, with a potential of merely 0.084 V vs. RHE at 10 0 0 mA cm-2 for HzOR and an overpotential of 74 mV at identical current density for HER, surpassing Pt/C by a substantial margin. Long-term durability assessments reveal stable operation over 10 0 0 h under high-current-density HzOR conditions. In a practical overall hydrazine splitting (OHzS) configuration, the electricity requirement for H2 generation stands at only 0.146 kWh m-3 at 100 mA cm-2 , which is a 92 % reduction compared to conventional water electrolysis (1.74 kWh m-3 H2 ). This study offers a viable electronic-structure engineering strategy for designing efficient and durable bifunctional electrocatalysts toward practical energy-saving H2 production. (c) 2026 Published by Elsevier Ltd on behalf of The editorial office of Journal of Materials Science & Technology.
