Coupled Variational Inequalities: Existence,Stability and Optimal Control

Journal of Optimization Theory and Applications - In this paper, we introduce and investigate a new kind of coupled systems, called coupled variational inequalities, which consist of two elliptic...     

Flower-like shaped Bi12TiO20/g-C3N4 heterojunction for effective elimination of organic pollutants: Preparation,characterization, and mechanism study

Flower-like shaped Bi₁₂TiO₂₀ (Bismuth Titanate)/g-C₃N₄ (graphite-like carbon nitride) heterojunction was prepared through hydrothermal and sonification methods for the degradation of organic pollutants by visible-light irradiation. The preparation process, chemical structures, and the mechanism of photocatalytic enhancement of the heterostructures were studied systematically. Under visible-light irradiation, the novel flower-like shaped Bi₁₂TiO₂₀/g-C₃N₄ heterojunction demonstrates prominent activities for the degradation of rhodamine B and p-nitrophenol, with the introduction of flower-like shaped Bi₁₂TiO₂₀ into g-C₃N₄ composites greatly increasing the activity of pure g-C₃N₄. This activity enhancement for the heterojunction could be mainly attributed to its low recombination speed of electron–hole pairs, high adsorption ability of organic pollutants, and better optical absorption ability. Moreover, in the visible-light system of Bi₁₂TiO₂₀/g-C₃N₄, ^•OH also contributed to the degradation of pollutants, which may explain the enhanced photocatalytic activity after the introduction of Bi₁₂TiO_20, as ^•OH is inactive in pure g-C₃N₄. Furthermore, 10 wt.% Bi₁₂TiO₂₀/g-C₃N₄ showed not only high activity but also good stability for degradation of aqueous organic pollutants, implying potential applications prospect.     

Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities

This paper considers a class of vector variational inequalities. First, we present an equivalent formulation, which is a scalar variational inequality, for the deterministic vector variational inequality. Then we concentrate on the stochastic circumstance. By noting that the stochastic vector variational inequality may not have a solution feasible for all realizations of the random variable in general, for tractability, we employ the expected residual minimization approach, which aims at minimizing the expected residual of the so-called regularized gap function. We investigate the properties of the expected residual minimization problem, and furthermore, we propose a sample average approximation method for solving the expected residual minimization problem. Comprehensive convergence analysis for the approximation approach is established as well.     

Calculus of directional coderivatives and normal cones in Asplund spaces

We study the directional Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings in Asplund spaces and establish extensive calculus results on these constructions under various operations of sets and mappings. We also develop calculus of the directional sequential normal compactness both in general Banach spaces and in Asplund spaces.     

Weak Differentiability with Applications to Variational Analysis

In this paper we first review the theory of weak differentiability with some improvements and unifications of existing results; then we introduce an extended variant of this notion and establish its basic properties; finally we use the weak differentiability and its variant to develop new calculus results in variational analysis for the theory of generalized differentiation and the sequential normal compactness. In this way we demonstrate that the weak differentiability and its variant, in contrast to the usual differentiability, are in fact more suitable for Fréchet and limiting/Mordukhovich constructions in variational analysis.     

18‐Crown‐6 promoting Pd/C‐catalyzed cross‐coupling reaction of aryl bromides and arylboronic acids in aqueous media

Pd/C‐catalyzed Suzuki–Miyaura cross‐coupling between aryl bromides and arylboronic acids in 50% methanol aqueous solution proceeded smoothly in the presence of 18‐crown‐6. Various aryl bromides bearing electron‐withdrawing groups and electron‐donating groups coupled with arylboronic acid in high yields. In addition, the catalyst could be recycled five times without loss of activity. Copyright © 2012 John Wiley & Sons, Ltd.