Inversions of Hölder’s Inequality

Mathematical Notes - In the present paper, new theorems on the inversion of the Hölder inequality that refine similar inversions known previously are proved.     

Two Ag(I)-Containing Supramolecular Coordination Polymers Constructed from the Multidentate N-donor Ligand 1-((1H-1,2,4-triazol-1-yl)methyl)-3,5-bis(3-pyridyl)-1,2,4-triazole Based on Hydrogen-Bonding and π–π Interactions: Syntheses,Crystal Structures,Optical Band Gaps and Luminescent Properties

Two Ag(I)-based coordination polymers, namely [Ag₂(3,3′-tmbpt)(o-Hbdc)₂]·H₂O (1) and [Ag₈(3,3′-tmbpt)₄(1,2,4-Hbtc)₄(H₂O)] (2) (3,3′-tmbpt?=?1-((1H-1,2,4-triazol-1-yl)methyl)-3,5-bis(3-pyridyl)-1,2,4-triazole, o-H₂bdc?=?1,2-benzenedicarboxylic acid and 1,2,4-H₃btc?=?1,2,4-benzenetricarboxylic acid), have been synthesized. Single-crystal X-ray diffraction analyses, elemental analyses, infrared spectra, powder X-ray diffraction analyses and thermogravimetric analyses have been carried out to characterize the structures of 1 and 2. Compound 1 shows a (3,4)-connected 2D layered structure with a Schläfli symbol of (4²·6)(4²·6³·8). The intermolecular O–H···O hydrogen-bonding interactions extend the 2D layer into a 3D supramolecular architecture. Compound 2 exhibits a (3,3)-connected double-layered structure with a Schläfli symbol of (4·8·10)₂(8²·10)₂. The intermolecular C–H···O hydrogen-bonding interactions link the double-layers to form a 3D supramolecular architecture. Moreover, there are intramolecular and intermolecular π–π interactions in 1 and 2, which stabilize the whole 3D supramolecular architectures. The band gaps of 1 and 2 are 3.19 and 3.09 eV, respectively, indicating the potential of 1 and 2 as semiconductive materials with wide band gaps. Moreover, 1 and 2 emit intense blue-green light, which may be potential photoactive materials.

Graphic Abstract

Two Ag(I)-based 3D supramolecular coordination polymers constructed from a multidentate N-donor ligand and two aromatic polycarboxylate anions via hydrogen-bonding and π–π interactions have been synthesized and characterized. The band gaps and photoluminescent properties of the compounds have been studied.

     

Meshfree simulations of large scale ductile fracture of stiffened ship hull plates during ship stranding

Meccanica - In this work, we have developed a systematic computational methodology to directly simulate the ductile fracture of ship hull structure during ship stranding based on the meshfree...     

Enhancement of Mass and Charge Transfer during Carbon Dioxide Photoreduction by Enhanced Surface Hydrophobicity without a Barrier Layer

The CO₂ reduction reaction (CRR) represents a promising route for the clean utilization of renewable resources. But mass-transfer limitations seriously hinder the forward step. Enhancing the surface hydrophobicity by using polymers has been proved to be one of the most efficient strategies. However, as macromolecular organics, polymers on the surface hinder the transfer of charge carriers from catalysts to reactants. Herein, we describe an in-situ surface fluorination strategy to enhance the surface hydrophobicity of TiO₂ without a barrier layer of organics, thus facilitating the mass transfer of CO₂ to catalysts and charge transfer. With less obstruction to charge transfer, a higher CO_2, and lower H⁺ surface concentration, the photocatalytic CRR generation rate of methanol (CH₃OH) is greatly enhanced to up to 247.15 μmol g⁻¹ h⁻¹. Furthermore, we investigated the overall defects; enhancing the surface hydrophobicity of catalysts provides a general and reliable method to improve the competitiveness of CRR.     

导电聚合物热电材料研究进展

导电聚合物在室温下具有较高的电导率(σ)、较低的热导率(κ)、柔韧性好、易于合成、原料来源丰富、对环境无污染等优势,是目前最具有热电应用潜力的有机热电材料之一。然而,目前针对导电聚合物作为有机热电材料的相关研究依然处于初级阶段,其在空气气氛中的化学稳定性问题、低的热电优值及尚未完全明确的热电机制一直困扰着研究人员。本文主要针对以上问题,在对前人的研究成果进行综述的基础上对目前有机热电材料所面临的关键问题进行阐述和总结。     

硫与Mn2O3空心球的复合结构及其在锂硫电池中的应用

在水热条件下,以碳球为模板合成了Mn₂O₃空心球,并用作锂硫电池的载硫基底材料。测试结果表明载硫量为51%的Mn₂O₃-S复合材料显示了较高的比容量,良好的循环稳定性和倍率性能。循环100圈后,最终可逆容量仍保持657 mA·g^-1,证明该Mn₂O₃空心球是一种有潜力的载硫基底材料。     

On Moments of Folded and Truncated Multivariate Normal Distributions

Recurrence relations for integrals that involve the density of multivariate normal distributions are developed. These recursions allow fast computation of the moments of folded and truncated multivariate normal distributions. Besides being numerically efficient, the proposed recursions also allow us to obtain explicit expressions of low-order moments of folded and truncated multivariate normal distributions. Supplementary material for this article is available online.     

关于刚体角速度定义的一个注解

给出了一种角速度定义方法. 这种方法基于固连坐标系基矢量和单位矢量的导数给出，但避免使用角速度矩阵概念. 另外从刚体上速度分布的角度，用速度场旋度的方法解释角速度. 可以帮助学生从另外一个角度来理解角速度概念.