MULTI-PARAMETER TIKHONOV REGULARIZATION FOR LINEAR ILL-POSED OPERATOR EQUATIONS

We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.

Electro-oxidation of Ni(Ⅱ)-citrate complexes at BDD electrode and simultaneous recovery of metallic nickel by electrodeposition

The simultaneous electro-oxidation of Ni(Ⅱ)-citrate and electrodeposition recovery of nickel metal were attempted in a combined electro-oxidation-electrodeposition reactor with a boron-doped diamond(BDD)anode and a polished titanium cathode.Effects of initial nickel citrate concentration,current density,initial p H,electrode spacing,electrolyte type,and initial electrolyte dosage on electrochemical performance were examined.The efficiencies of Ni(Ⅱ)-citrate removal and nickel metal recovery were determined to be 100%and over 72%,respectively,under the optimized conditions(10 m A/cm^(2),pH 4.09,80 mmol/L Na_(2)SO_(4),initial Ni(Ⅱ)-citrate concentration of 75 mg/L,electrode spacing of 1 cm,and 180 min of electrolysis).Energy consumption increased with increased current density,and the energy consumption was 0.032 kWh/L at a current density of 10 m A/cm^(2)(pH 6.58).The deposits at the cathode were characterized by scanning electron microscopy(SEM),energy-dispersive spectrometry(EDS),X-ray diffraction(XRD),and X-ray photoelectron spectroscopy(XPS).These characterization results indicated that the purity of metallic nickel in cathodic deposition was over 95%.The electrochemical system exhibited a prospective approach to oxidize metal complexes and recover metallic nickel.