Oxygen electrocatalysis has aroused considerable interest over the past years because of the new energy technologies boom in hydrogen energy and metal–air battery. However, due to the sluggish kinetic of the four‐electron transfer process in oxygen reduction reaction and oxygen evolution reaction, the electro‐catalysts are urgently needed to accelerate the oxygen electrocatalysis. Benefit from the high atom utilization efficiency, unprecedentedly high catalytic activity, and selectivity, single‐atom catalysts (SACs) are considered the most promising candidate to replace the traditional Pt‐group‐metal catalysts. Compared with SACs, the dual‐atom catalysts (DACs) are attracting more attraction including higher metal loading, more versatile active sites, and excellent catalytic activity. Therefore, it is essential to explore the new universal methods approaching to the preparation, characterization, and to elucidate the catalytic mechanisms of the DACs. In this review, several general synthetic strategies and structural characterization methods of DACs are introduced and the involved oxygen catalytic mechanisms are discussed. Moreover, the state‐of‐the‐art electrocatalytic applications including fuel cells, metal–air batteries, and water splitting have been sorted out at present. The authors hope this review has given some insights and inspiration to the researches about DACs in electro‐catalysis.

Aqueous Zn-ion batteries (ZIBs) have attracted ever-increasing attention because of their features of a cheaper cost, high safety level, and environment protection. Manganesebased oxides stand out among the many cathode material candidates because of their high voltage platform (1.4 V vs Zn 2+ /Zn). Nevertheless, manganese ion dissolution still is an essential issue in the application of manganese-based cathodes, and the strategy of using manganese ion dissolution to activate electrode materials is rarely achieved. Here, a high-capacity and stable binder-free MnO@CC cathode was prepared by facile electrochemical deposition and carbothermal reduction methods. Based on the MnO@CC cathode and a homemade gel polymer electrolyte, a flexible quasi-solid state ZIB was assembled and exhibited a high reversible capacity, a significant energy output of 345 Wh kg −1 , and excellent long-term cycling performance. The ultradispersed and well-crystallized octahedral MnO nanoparticle provides an improved ion transfer interface, and abundant Mn vacancy during the initial charging process provides sufficient inserted channels and available active sites for subsequent ion insertion and storage. In addition, for the as-activated MnO@CC electrode, the reversible coinsertion mechanism (H + and Zn 2+ ) is also monitored in the aqueous ZIBs. This work may provide insights into manufacturing advanced flexible aqueous ZIBs for wearable electronics via defect engineering.

We obtain a priori interior Hessian estimates to the special Lagrangian equation on general phases with constraints. Our results extend the classical conclusion that the estimates hold when the phase is critical/supercritial.

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