Highly Efficient,Green, and Scalable β‐Cyclodextrin‐Assisted Aqueous Exfoliation of Transition‐Metal Dichalcogenides: MoS2 and ReS2 Nanoflakes

The β‐cyclodextrin‐assisted aqueous‐exfoliation method was used to prepare transition‐metal dichalcogenide (TMD) nanosheets, in a cheap, highly efficient, scalable and environmentally friendly manner. As study cases, MoS₂ and ReS₂ nanoflakes were prepared according to this method. Particularly, the effective exfoliation of ReS₂ crystals in an aqueous environment was observed for the first time. Moreover, exfoliated nanomaterials can be readily utilized in hydrogen evolution reactions (HERs) as noble‐metal‐free catalysts. This work provides new opportunities for highly efficient exfoliation of TMDs and other 2D nanomaterials into few‐layer nanosheets in aqueous media. Their production process showed high biocompatibility, broad applicability and excellent sustainability.     

Molten Ag2SO4‐based Ion‐Exchange Preparation of Ag0.5La0.5TiO3 for Photocatalytic O2 Evolution

Ag_0.5La_0.5TiO₃ with an ABO₃ perovskite structure was synthesized by a newly developed ion‐exchange method. Molten Ag₂SO₄ instead of traditional molten AgNO₃ was used as Ag⁺ source in view of its high decomposition temperature (1052 °C), thereby guaranteeing the complete substitution of Ag⁺ for Na⁺ in Na_0.5La_0.5TiO₃ with a stable ABO₃ perovskite structure at a high ion‐exchange temperature (700 °C). Under full‐arc irradiation, the O₂‐evolution activity of Ag_0.5La_0.5TiO₃ was about 1.6 times that of Na_0.5La_0.5TiO₃ due to the optimized electronic band structures and local lattice structures. On the one hand, the substitution of Ag⁺ for Na⁺ elevated the VBM and thus narrowed the band gap from 3.19 to 2.83 eV, thereby extending the light‐response range and, accordingly, enhancing the photoexcitation to generate more charge carriers. On the other hand, the substitution of Ag⁺ for Na⁺ induced a lattice distortion of the ABO₃ perovskite structure, thereby promoting the separation and migration of charge carriers. Moreover, under visible‐light irradiation, Ag_0.5La_0.5TiO₃ displayed notable O₂ evolution whereas Na_0.5La_0.5TiO₃ showed little O₂ evolution, thus demonstrating that the substitution of Ag⁺ for Na⁺ enabled the use of visible light to evolve O₂ photocatalytically. This work presents an effective route to explore novel Ag‐based photocatalysts.     

The analysis study on nonlinear iterative methods for inverse problems

In this paper, the nonlinear iterative methods, which are different from the classical algorithms, to solve inverse problems are presented. Our methods by denoting some parameters and some properties of the algorithm in both noise and noiseless cases are studied. Finally, the convergence of the sequence generated by the algorithm without noise is discussed.     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.     

Remarks on Neumann boundary problems involving Jacobians

In this note, we explore the validity of Wente-type estimates for Neumann boundary problems involving Jacobians. We show in particular that such estimates do not in general hold under the same hypotheses on the data for Dirichlet boundary problems.     

Calderón problem for connections

In this paper, we consider the problem of identifying a connection ? on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian ?*? over conformally transversally anisotropic (CTA) manifolds. This was proved in [9 Dos Santos Ferreira, D., Kenig, C., Salo, M., Uhlmann, G. (2009). Limiting Carleman weights and anisotropic inverse problems. Invent. Math. 178:119–171.[Crossref], [Web of Science ®] , [Google Scholar]] for line bundles in the case of the transversal manifold being simple—we generalize this result to the case where the transversal manifold only has an injective ray transform. Moreover, the construction of suitable Gaussian beam solutions on vector bundles is given for the case of the connection Laplacian and a potential, following the works of [11 Dos Santos Ferreira, D., Kurylev, Y., Lassas, M., Salo, M. (2016). The Calderón problem in transversally anisotropic geometries. J. Eur. Math. Soc., 18:2579–2626.[Crossref], [Web of Science ®] , [Google Scholar]]. This in turn enables us to construct the Complex Geometrical Optics (CGO) solutions and prove our main uniqueness result. We also reduce the problem to a new non-abelian X-ray transform for the case of simple transversal manifolds and higher rank vector bundles. Finally, we prove the recovery of a flat connection in general from the DN map, up to gauge equivalence, using an argument relating the Cauchy data of the connection Laplacian and the holonomy.     

A note on functional a posteriori estimates for elliptic optimal control problems

In this work, new results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed, and fully computable lower bounds for the cost functional in addition to the already existing upper bounds. Using both, the lower and the upper bounds, we arrive at two‐sided estimates for the cost functional. We prove that these bounds finally lead to sharp, guaranteed and fully computable upper estimates for the discretization error in the state and the control of the optimal control problem. First numerical tests are presented confirming the efficiency of the a posteriori estimates derived. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 403–424, 2017