Enhancing Hydrogen Generation Through Nanoconfinement of Sensitizers and Catalysts in a Homogeneous Supramolecular Organic Framework.

Enrichment of molecular photosensitizers and catalysts in a confined nanospace is conducive for photocatalytic reactions due to improved photoexcited electron transfer from photosensitizers to catalysts. Herein, the self-assembly of a highly stable 3D supramolecular organic framework from a rigid bipyridine-derived tetrahedral monomer and cucurbit[8]uril in water, and its efficient and simultaneous intake of both [Ru(bpy)3 ]2+ -based photosensitizers and various polyoxometalates, that can take place at very low loading, are reported. The enrichment substantially increases the apparent concentration of both photosensitizer and catalyst in the interior of the framework, which leads to a recyclable, homogeneous, visible light-driven photocatalytic system with 110-fold increase of the turnover number for the hydrogen evolution reaction

Hinge solitons in three-dimensional second-order topological insulators

A second-order topological insulator in three dimensions refers to a topological insulator with gapless states localized on the hinges, which is a generalization of a traditional topological insulator with gapless states localized on the surfaces. Here we theoretically demonstrate the existence of stable solitons localized on the hinges of a second-order topological insulator in three dimensions when nonlinearity is involved. By means of systematic numerical study, we find that the soliton has strong localization in real space and propagates along the hinge unidirectionally without changing its shape. We further construct an electric network to simulate the second-order topological insulator. When a nonlinear inductor is appropriately involved, we find that the system can support a bright soliton for the voltage distribution demonstrated by stable time evolution of a voltage pulse.Comment: 11 pages, 6 figure

Hermite–Hadamard-Type Integral Inequalities for Functions Whose First Derivatives are Convex

We establish some new Hermite–Hadamard-type inequalities for functions whose first derivatives are of convexity and apply these inequalities to construct inequalities for special means.Встановлено дєякі нові нєрівності типу Ерміта - Адамара для Функцій, похідні яких мають опуклість. Ці нєрівності застосовано при побудові нерівностей для спеціальних середніх