Resolvents and Yosida Approximations of Displacement Mappings of Isometries

Set-Valued and Variational Analysis - Maximally monotone operators are fundamental objects in modern optimization. The main classes of monotone operators are subdifferential operators and matrices...     

Modification of Kraft Lignin with Dodecyl Glycidyl Ether

Kraft lignin (KL) is extensively produced in industry but is mainly burned as fuel. To broaden its use, KL was grafted with dodecyl glycidyl ether to alter its thermal properties. The reaction of KL with dodecyl glycidyl ether (DGE) was analyzed using nuclear magnetic resonance (NMR), Fourier infrared spectroscopy (FT-IR) and elemental analysis. Alternatively, KL was methylated to mask its phenolic hydroxy groups to investigate how phenolic hydroxy groups impact the grafting of the alkyl chain of DGE onto lignin (methylated Kraft lignin, MKL). The methylation facilitated the molecular weight enhancement and thermal stability reduction of Kraft lignin via grafting with DGE. The influence of grafting alkyl chains on the structural and thermal properties of KL and MKL was studied using thermogravimetric analysis and differential scanning calorimetry analysis. Our data suggest that, due to their high molecular weights and lower glass transition temperatures, the produced lignin derivatives may be promising feedstocks for composite production.     

On the asymptotic behaviour of the Aragón Artacho–Campoy algorithm

Aragón Artacho and Campoy recently proposed a new method for computing the projection onto the intersection of two closed convex sets in Hilbert space; moreover, they proposed in 2018 a generalization from normal cone operators to maximally monotone operators. In this paper, we complete this analysis by demonstrating that the underlying curve converges to the nearest zero of the sum of the two operators. We also provide a new interpretation of the underlying operators in terms of the resolvent and the proximal average.