Oxygen reduction/evolution reactions (ORR/OERs) catalysts play a key role in the metal‐air battery and water‐splitting process. Herein, we developed a facile template‐free method to fabricate a new type of non–noble metal‐based hybrid catalyst which consists of binary FeNi alloy/nitride nanocrystals with graphitic‐shell and biomass‐derived N‐doped carbon (NC) (FexNiyN@C/NC). This novel nanostructure exhibits superior performance for ORR/OER, which can be attributed to the strong interactions between the graphitic‐shell encapsulated FeNi alloy/nitride nanocrystals and the N‐doped porous carbon substrate. The X‐ray absorption spectroscopy technique was employed to reveal the underlying mechanisms for the excellent performance. The assembled Zn‐air battery device exhibits outstanding charging/discharging performance and cycling stability, indicating the great potential of this type of novel catalysts.
We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions which we call generalized self-concordant functions. This notion allows us to develop a unified framework for designing Newton-type methods to solve convex optimization problems. The proposed theory provides a mathematical tool to analyze both local and global convergence of Newton-type methods without imposing unverifiable assumptions as long as the underlying functionals fall into our class of generalized self-concordant functions. First, we introduce the class of generalized self-concordant functions which covers the class of standard selfconcordant functions as a special case. Next, we establish several properties and key estimates of this function class which can be used to design numerical methods. Then, we apply this theory to develop several Newton-type methods for solving a class of smooth convex optimization problems involving generalized self-concordant functions. We provide an explicit step-size for a damped-step Newton-type scheme which can guarantee a global convergence without performing any globalization strategy. We also prove a local quadratic convergence of this method and its full-step variant without requiring the Lipschitz continuity of the objective Hessian mapping. Then, we extend our result to develop proximal Newton-type methods for a class of composite convex minimization problems involving generalized self-concordant functions. We also achieve both global and local convergence without additional assumptions. Finally, we verify our theoretical results via several numerical examples, and compare them with existing methods.
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