单层MXene纳米片Ti2N电磁特性的过渡金属(Sc、V、Zr)掺杂效应

二维材料MXene纳米片由于具有较大的比表面积和较高的电子迁移率而受到广泛的关注。本文采用基于密度泛函理论的第一性原理计算,对单层MXene纳米片Ti₂N电磁特性的过渡金属(Sc、V、Zr)掺杂效应进行了系统研究。结果表明,所有过渡金属掺杂体系结合能均为负值,结构均稳定;其中Ti₂N-Sc体系的形成能为-2.242 eV,结构更易形成,且保持稳定;掺杂后Ti₂N-Sc、Ti₂N-Zr体系磁矩增大;此外,Ti₂N-Sc体系中保留了较高的自旋极化率,达到84.9%,可预测该体系在自旋电子学中具有潜在的应用价值。     

Synthesis and Diverse Transformations of a Dinitrogen Dititanium Hydride Complex Bearing Rigid Acridane-Based PNP-Pincer Ligands

Studies on N₂ activation and transformation by transition metal hydride complexes are of particular interest and importance. The synthesis and diverse transformations of a dinitrogen dititanium hydride complex bearing the rigid acridane-based ^acriPNP-pincer ligands {[(^acriPNP)Ti]₂(μ₂-η¹:η²-N₂)(μ₂-H)₂} are presented. This complex enabled N₂ cleavage and hydrogenation even without additional H₂ or other reducing agents. Furthermore, diverse transformations of the N₂ unit with a variety of organometallic compounds such as ZnMe₂, MgMe₂, AlMe₃, B(C₆F₅)₃, PinBH, and PhSiH₃ have been well established at the rigid ^acriPNP-ligated dititanium framework, such as reversible bonding-mode change between the end-on and side-on/end-on fashions, diborylative N=N bond cleavage, the formal insertion of two dimethylaluminum species into the N=N bond, and the formal insertion of two silylene units into the N=N bond. This work has revealed many unprecedented aspects of dinitrogen reaction chemistry.     

Homogeneous variable exponent Besov and Triebel–Lizorkin spaces

We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.     

An organoantimony nitrate complex with azastibocine framework as water tolerant Lewis acid catalyst for the synthesis of 1,2-disubstitued benzimidazoles

A novel organoantimony complex of 6-cyclohexyl-6,7-dihydrodibenzo[c,f] [1,5]azastibocin-12(5H)-yl nitrate ( 2 ) was synthesized and systematically characterized by techniques such as NMR spectra, TG-DSC, and X-ray diffraction. It was found that the complex 2 exhibits relatively strong Lewis acidity (3.3 < Ho ≤ 4.8) and could be employed as a water tolerant Lewis acid catalyst for the synthesis of synthetically valuable benzimidazole derivatives starting from aldehydes and arylenediamines. This catalytic system shows excellent tolerance toward a wide variety of functional groups, such as methyl, methoxyl, fluoro, chloro, bromo, nitro, cyan, trifluoromethyl, 1-naphthaldehyde, furfural and n-butyl, together with facile reusability in 5 times scale enlarged synthesis.     

Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.     

Advantageous Interfacial Effects of AgPd/g-C3N4 for Photocatalytic Hydrogen Evolution: Electronic Structure and H2O Dissociation

Bimetallic AgPd nanoparticles have been synthesized before, but the interfacial electronic effects of AgPd on the photocatalytic performance have been investigated less. In this work, the results of hydrogen evolution suggest that the bimetallic AgPd/g-C₃N₄ sample has superior activity to Ag/g-C₃N₄ and Pd/g-C₃N₄ photocatalysts. The UV/Vis diffuse reflectance spectroscopy, X-ray photoelectron spectroscopy, CO adsorption diffuse reflectance FTIR spectroscopy, and FTIR results demonstrate that in the AgPd/g-C₃N₄, the surface electronic structures of Pd and Ag are changed, which is beneficial for faster photogenerated electron transfer and greater H₂O molecule adsorption. In situ ESR spectra suggest that, under visible light irradiation, there is more H₂O dissociation to radical species on the AgPd/g-C₃N₄ photocatalyst. Furthermore, DFT calculations confirm the interfacial electronic effects of AgPd/g-C₃N₄, that is, Pd^δ−⋅⋅⋅Ag^δ+, and the activation energy of H₂O molecule dissociation on AgPd/g-C₃N₄ is the lowest, which is the main contributor to the enhanced photocatalytic H₂ evolution.     

The martingale problem for a class of nonlocal operators of diagonal type

We consider systems of stochastic differential equations of the form $$\begin{array}{c}\hfill d{X}_t^i=\sum _{j=1}^d{A}_{ij}\left(X_{t?}\right)d{Z}_t^j\end{array}$$ for $i=1,?,d$ with continuous, bounded and non‐degenerate coefficients. Here $Z_t^1,?,Z_t^d$ are independent one‐dimensional stable processes with ${\alpha }_1,?,{\alpha }_d\in (0,2)$. In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices.