A CCBM-based generalized GKB iterative regularizing algorithm for inverse Cauchy problems

This paper examines inverse Cauchy problems that are governed by a kind of elliptic partial differential equation. The inverse problems involve recovering the missing data on an inaccessible boundary from the measured data on an accessible boundary, which is severely ill-posed. By using the coupled complex boundary method (CCBM), which integrates both Dirichlet and Neumann data into a single Robin boundary condition, we reformulate the underlying problem into an operator equation. Based on this new formulation, we prove the existence of a unique solution even in cases with noisy data. A Golub-Kahan bidiagonalization (GKB) process together with Givens rotation is employed for iteratively solving the proposed operator equation. The regularizing property of the developed method, called CCBM-GKB, and its convergence rate results are proved under a posteriori stopping rule. Finally, a linear finite element method is used for the numerical realization of CCBM-GKB. Various numerical experiments demonstrate that CCBM-GKB is a kind of accelerated iterative regularization method, as it is much faster than the classic Landweber method

CNx-modified Fe3O4 as Pt nanoparticle support for the oxygen reduction reaction

A novel electrocatalyst support material, nitrogendoped carbon (CNx)-modified Fe3O4 (Fe3O4-CNx), was synthesized through carbonizing a polypyrrole-Fe3O4 hybridized precursor. Subsequently, Fe3O4-CNx-supported Pt (Pt/Fe3O4-CNx) nanocomposites were prepared by reducing Pt precursor in ethylene glycol solution and evaluated for the oxygen reduction reaction (ORR). The Pt/Fe3O4-CNx catalysts were characterized by X-ray diffraction, Raman spectra, X-ray photoelectron spectroscopy, scanning electron microscopy, and transmission electron microscopy. The electrocatalytic activity and stability of the as-prepared electrocatalysts toward ORR were studied by cyclic voltammetry and steady-state polarization measurements. The results showed that Pt/ Fe3O4-CNx catalysts exhibited superior catalytic performance for ORR to the conventional Pt/C and Pt/C-CNx catalysts.Web of Scienc