Local and parallel finite element algorithm for stationary incompressible magnetohydrodynamics

This article presents a local and parallel finite element method for the stationary incompressible magnetohydrodynamics problem. The key idea of this algorithm comes from the two‐grid discretization technique. Specifically, we solve the nonlinear system on a global coarse mesh, and then solve a series of linear problems on several subdomains in parallel. Furthermore, local a priori estimates are obtained on a general shape regular grid. The efficiency of the algorithm is also illustrated by some numerical experiments.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1513–1539, 2017     

双调和算子特征值问题的混合三角谱元方法

本文针对双调和算子特征值问题设计了基于混合变分形式的三角谱元逼近格式,其基函数采用指标为(-1,-1,-1)的广义Koornwinder多项式.在H~1-及H_0~1-正交谱元投影的逼近理论基础上,我们建立了双调和算子特征值与特征函数的收敛性估计;它关于网格尺寸h是最优的,关于多项式次数M是次优的.然而,在H_0~2-正交谱元投影的最优估计假设前提下,关于M的次优收敛阶估计则提升为最优.此外,Koornwinder分片多项式逼近的结果还表明,在带权Besov空间范数的度量下,对于存在着区域角点奇性的双调和算子特征值问题,谱元方法的收敛阶能达到h-型有限元方法的2倍.最后,本文的数值实验结果展示了谱元逼近格式的高效性,同时也验证了相关理论的正确性.     

5-正则图的全控制数的一个注记

设G是不含孤立点的图,S是G的一个顶点子集,若G的每一个顶点都与S中的某顶点邻接,则称S是G的全控制集.G的最小全控制集所含顶点的个数称为G的全控制数,记为γt(G).Thomasse和Yeo证明了若G是最小度至少为5的n阶连通图,则γt(G)≤17n/44.在5-正则图上改进了Thomasse和Yeo的结论,证明了若G是n阶5-正则图,则,γt(G)≤106n/275.     

Distance domination of generalized de Bruijn and Kautz digraphs

Let G = (V,A) be a digraph and k ≥ 1 an integer. For u, v ∈ V, we say that the vertex u distance k-dominate v if the distance from u to v at most k. A set D of vertices in G is a distance k-dominating set if each vertex of V D is distance k-dominated by some vertex of D. The distance k-domination number of G, denoted by γ _k (G), is the minimum cardinality of a distance k-dominating set of G. Generalized de Bruijn digraphs G _B (n, d) and generalized Kautz digraphs G _K (n, d) are good candidates for interconnection networks. Denote Δ _k := (∑ _j=0 ^k d ^j )^?1. F. Tian and J. Xu showed that ?nΔ _k ? γ _k (G _B (n, d)) ≤?n/d ^k? and ?nΔ _k ? ≤ γ _k (G _K (n, d)) ≤ ?n/d ^k ?. In this paper, we prove that every generalized de Bruijn digraph G _B (n, d) has the distance k-domination number ?nΔ _k ? or ?nΔ _k ?+1, and the distance k-domination number of every generalized Kautz digraph G _K (n, d) bounded above by ?n/(d ^k?1+d ^k )?. Additionally, we present various sufficient conditions for γ _k (G _B (n, d)) = ?nΔ _k ? and γ _k (G _K (n, d)) = ?nΔ _k ?.     

Semiparametric Bayesian inference for mean-covariance regression models

In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.     

Oxidation-Reduction Molecular Junction Covalent Organic Frameworks for Full Reaction Photosynthesis of H2O2

The full reaction photosynthesis of H₂O₂ that can combine water-oxidation and oxygen-reduction without sacrificial agents is highly demanded to maximize the light-utilization and overcome the complex reaction-process of anthraquinone-oxidation. Here, a kind of oxidation-reduction molecular junction covalent-organic-framework (TTF-BT-COF) has been synthesized through the covalent-coupling of tetrathiafulvalene (photo-oxidation site) and benzothiazole (photo-reduction site), which presents visible-light-adsorption region, effective electron-hole separation-efficiency and photo-redox sites that enables full reaction generation of H₂O₂. Specifically, a record-high yield (TTF-BT-COF, ≈276 000 μM h⁻¹ g⁻¹) for H₂O₂ photosynthesis without sacrificial agents has been achieved among porous crystalline photocatalysts. This is the first work that can design oxidation-reduction molecular junction COFs for full reaction photosynthesis of H₂O₂, which might extend the scope of COFs in H₂O₂ production.     

Semiconductor SERS on Colourful Substrates with Fabry-Pérot Cavities

Non-metallic materials have emerged as a new family of active substrates for surface-enhanced Raman scattering (SERS), with unique advantages over their metal counterparts. However, owing to their inefficient interaction with the incident wavelength, the Raman enhancement achieved with non-metallic materials is considerably lower with respect to the metallic ones. Herein, we propose colourful semiconductor-based SERS substrates for the first time by utilizing a Fabry-Pérot cavity, which realize a large freedom in manipulating light. Owing to the delicate adjustment of the absorption in terms of both frequency and intensity, resonant absorption can be achieved with a variety of non-metal SERS substrates, with the sensitivity further enhanced by ≈100 times. As a typical example, by introducing a Fabry-Pérot-type substrate fabricated with SiO₂/Si, a rather low detection limit of 10⁻¹⁶ M for the SARS-CoV-2S protein is achieved on SnS₂. This study provides a realistic strategy for increasing SERS sensitivity when semiconductors are employed as SERS substrates.     

Frenkel Defect-modulated Anti-thermal Quenching Luminescence in Lanthanide-doped Sc2(WO4)3

Although large amount of effort has been invested in combating thermal quenching that severely degrades the performance of luminescent materials particularly at high temperatures, not much affirmative progress has been realized. Herein, we demonstrate that the Frenkel defect formed via controlled annealing of Sc₂(WO₄)₃:Ln (Ln=Yb, Er, Eu, Tb, Sm), can work as energy reservoir and back-transfer the stored excitation energy to Ln³⁺ upon heating. Therefore, except routine anti-thermal quenching, thermally enhanced 415-fold downshifting and 405-fold upconversion luminescence are even obtained in Sc₂(WO₄)₃:Yb/Er, which has set a record of both the Yb³⁺-Er³⁺ energy transfer efficiency (>85 %) and the working temperature at 500 and 1073 K, respectively. Moreover, this design strategy is extendable to other hosts possessing Frenkel defect, and modulation of which directly determines whether enhanced or decreased luminescence can be obtained. This discovery has paved new avenues to reliable generation of high-temperature luminescence.     

Analysis of steroidal glycoalkaloids and their metabolites in Solanum nigrum fruits based on liquid chromatography-tandem mass spectrometry and molecular networking

Solanum nigrum fruit is like a treasure house for anticancer drugs because of its steroidal alkaloids. However, the clinical treatment of cancer mainly uses immature fruits, which can cause a toxic reaction if eaten directly, while mature fruits are eaten as fruit. In order to clarify the reasons for the differences in pharmacodynamics and toxicity between them, we studied the composition and metabolism of steroidal alkaloids in fruits of different maturities based on liquid chromatography-tandem mass spectrometry and molecular networking. As a result, 114 steroidal glycoalkaloids were identified. During fruit ripening, the aglycones of steroidal alkaloids mainly undergo hydroxylation and carboxylation, and the sugar side chains mainly undergo acylation and glycosylation reactions. Furthermore, 219 steroidal alkaloids were identified in a metabolism experiment in rats. Metabolic processes include deglycosylation, redox, sulfuric acid binding, acetyl binding, and glucuronic acid-binding. Steroidal alkaloids in mature fruits have high molecular weight and polarity, which are difficult to absorb, and most of them are excreted through feces and urine, which may be the reason for their poor efficacy. This study lays a foundation for research on the biosynthesis of steroidal alkaloids and provides potential candidates for the discovery of new steroidal alkaloid anticancer drugs.