Nucleophilic Aromatic Substitution of Unactivated Aryl Fluorides with Primary Aliphatic Amines by Organic Photoredox Catalysis

In this work, a mild and transition-metal-free approach for the nucleophilic aromatic substitution (S_NAr) of unactivated fluoroarenes with primary aliphatic amines to form aromatic amines is reported. This reaction is facilitated by the formation of cationic fluoroarene radical intermediates in the presence of an acridinium-based organic photocatalyst under blue-light irradiation. Various electron-rich and electron-neutral fluoroarenes are competent electrophiles for this transformation. A wide range of primary aliphatic amines, including amino acid esters, dipeptides, and linear and branched amines are suitable nucleophiles. The synthetic utility of this protocol is demonstrated by the late-stage functionalization of several complex drug molecules.     

On a Spanning K-tree Containing Specified Vertices in a Graph

Acta Mathematicae Applicatae Sinica, English Series - A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in...     

Phase transition layers with boundary intersection for an inhomogeneous Allen–Cahn equation

We consider the nonlinear problem of inhomogeneous Allen–Cahn equation

${?}^2\mathrm{\Delta }u+V(y)u(1?u^2)=0\text{in}\mathrm{\Omega },\frac{?u}{?\nu }=0\text{on}?\mathrm{\Omega },$

where Ω is a bounded domain in ${\mathbb{R}}^2$ with smooth boundary, ? is a small positive parameter, ν denotes the unit outward normal of ?Ω, V is a positive smooth function on $\overline{\mathrm{\Omega }}$. Let Γ be a curve intersecting orthogonally with ?Ω at exactly two points and dividing Ω into two parts. Moreover, Γ satisfies stationary and non-degenerate conditions with respect to the functional ${\int }_{\mathrm{\Gamma }}{V}^{1/2}$. We can prove that there exists a solution $u_{?}$ such that: as $?\to 0$, $u_{?}$ approaches +1 in one part of Ω, while tends to ?1 in the other part, except a small neighborhood of Γ.     

Iodine/persulfate-promoted site-selective direct thiolation of quinolones and uracils

A simple and general method for direct thiolation of 4-quinolones with disulfides or thiols under I₂/K₂S₂O₈ system has been developed. Under the optimal conditions, the C–S bond coupling can take place effectively with good to decent yields and excellent regioselectivity of the S-linked products. The established metal-free site-selective approach was also applicable to transform a range of uracil substrates to the thio-substituted products under mild conditions. Further transformation to the sulfone derivatives can be conveniently performed in one-pot. These easy-to-handle protocols represent a useful and interesting synthetic alternative with good substrate scope and functional group compatibility.     

RHIC-STAR重离子碰撞实验中可鉴别粒子的集体流研究

本文总结了RHIC-STAR重离子碰撞实验中近年来重要的空间各向异性流的结果。主要包括最高能量重离子碰撞中多重奇异及含粲夸克粒子椭圆流的结果和RHIC能量扫描计划BES-I中椭圆流和直接流的结果，其中金金碰撞54.4和27 GeV是最新测量结果。我们发现新碰撞能量点的直接流符合碰撞能量依赖的总体趋势；椭圆流符合组分夸克标度性，这表明54.4和27 GeV的金金碰撞中形成了部分子层次的集体运动。同时展望了未来能量扫描实验的计划以及与之对应的空间各向异性流的研究重点。     

光驱动C1转换到高附加值化学品的研究进展

阐述了光驱动C1化学的最新研究进展, 分别对光驱动费托合成、 水煤气变换、 二氧化碳加氢、 甲烷重整和甲醇重整制氢的研究进行了综述, 提出了当前研究存在的问题及发展方向.     

Hermitian adjacency matrix of the second kind for mixed graphs

This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind (N-matrix for short) introduced by Mohar [25]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u to v is equal to the sixth root of unity $\omega =\frac{1+\mathbf{i}\sqrt{3}}{2}$ (and its symmetric entry is $\overline{\omega }=\frac{1?\mathbf{i}\sqrt{3}}{2}$); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. The main results of this paper include the following: equivalent conditions for a mixed graph that shares the same spectrum of its N-matrix with its underlying graph are given. A sharp upper bound on the spectral radius is established and the corresponding extremal mixed graphs are identified. Operations which are called two-way and three-way switchings are discussed–they give rise to some cospectral mixed graphs. We extract all the mixed graphs whose rank of its N-matrix is 2 (resp. 3). Furthermore, we show that if $M_G$ is a connected mixed graph with rank 2, then $M_G$ is switching equivalent to each connected mixed graph to which it is cospectral. However, this does not hold for some connected mixed graphs with rank 3. We identify all mixed graphs whose eigenvalues of its N-matrix lie in the range $(?\alpha ,\alpha )$ for $\alpha \in \{\sqrt{2},\sqrt{3},2\}$.