On the rainbow matching conjecture for 3-uniform hypergraphs

Aharoni and Howard and, independently, Huang et al. (2012) proposed the following rainbow version of the Erdős matching conjecture: For positive integers n, k and m with n ⩾ km, if each of the families \(F_{1},\ldots,F_{m}\subseteq\left(\begin{array}{c}[n]\\ k\end{array}\right)\) has size more than \(\max\{\left(\begin{array}{c}n\\ k\end{array}\right)-\left(\begin{array}{c}n-m+1\\ k\end{array}\right),\left(\begin{array}{c}km-1\\ k\end{array}\right)\}\), then there exist pairwise disjoint subsets e₁,…,e_m such that e_i ∈ F_i for all i ∈ [m]. We prove that there exists an absolute constant n₀ such that this rainbow version holds for k = 3 and n ⩾ n₀. We convert this rainbow matching problem to a matching problem on a special hypergraph H. We then combine several existing techniques on matchings in uniform hypergraphs: Find an absorbing matching M in H; use a randomization process of Alon et al. (2012) to find an almost regular subgraph of H − V(M); find an almost perfect matching in H − V(M). To complete the process, we also need to prove a new result on matchings in 3-uniform hypergraphs, which can be viewed as a stability version of a result of Łuczak and Mieczkowska (2014) and might be of independent interest.

     

微区X射线荧光成像技术在岩心分析中的应用

微区X射线荧光（Micro-XRF）分析技术是通过微小的X射线光束照射样品，对样品进行原位成分观测的无损分析手段之一，具有灵敏度高、速度快和准确性高的特点。采用微区X射线荧光光谱仪（M6 JETSTREAM）对安徽铜陵冬瓜山铜矿床四段岩心样品进行面扫描，分析不同矿层共17种元素区域分布特征、空间分布规律及组合关系等，结果表明：（1）Cu和Fe两种成矿元素高值空间分布区域基本不重叠，S与Fe分布范围高度重叠，关系密切，微量元素Ni，Bi，Pb，Zn，Si，Na与Cu密切相关，而Ti，Al，K与Fe具有弱相关性；（2）垂向上，Fe元素含量随深度增加逐步增大，而Cu元素含量呈降低趋势，其他元素也随深度呈下降趋势；（3）元素分布受石炭纪中期海底喷流沉积成矿作用和岩浆热液成矿作用叠加改造作用明显；（4）该钻孔矿石矿物以磁黄铁矿、黄铜矿和黄铁矿为主，垂向上组合规律明显，脉石矿物以石英、石榴子石和透辉石为主。该技术通过分析元素空间分布规律、相关性以及矿物组合和分配关系等可对元素富集和运移以及对矿床的成矿机制、成因模式等地质环境和地质过程提供新认识和新证据。结合矿床地球化学特征的分布模式，微量元素可作为寻找主矿种的指示元素，为深部找矿提供依据。此外，该技术能作为预分析技术快速筛选出感兴趣的信息和位置，为后期各种更高精度的微区分析提供不同尺度、不同层次的元素分布信息。     

Base-promoted N-alkylation using formamides as the N-sources in neat water

An efficient catalyst-free, alternative method for the C–N bond formation reaction of alkyl electrophiles using formamides as the N-sources was achieved under mild conditions. The reaction possesses the advantages of a broad range of substrates scope and wide functional group tolerance. It should also be noted that this process was performed using the environmentally benign water as the sole solvent, and high yield can also be achieved in ten-gram scale.     

Preparing L‐α‐Glycerophosphocholine in a Phase‐Transfer Catalytic Reaction: Kinetic Study

The transesterification of phosphatidylcholine with methanol was successfully carried out using a promising solvent methyl tert‐butyl ether instead of traditional ether, and the reaction was dramatically enhanced in the presence of tetrabutylammonium hydroxide as the phase‐transfer catalyst. Kinetics of the reaction including the effects of the reaction conditions on the conversion of phosphatidylcholine and the apparent rate constant (k_app) were investigated in detail. On the basis of the experimental evidence, the transesterification mechanism was proposed and a kinetic model was developed, and the experimental data were well described by the pseudo–first‐order equation.     

Nonrigid image registration using similarity measure based on spatially weighted global probability distribution function

In nonrigid image registration, similarity measures including spatial information have been shown to perform better than those measures without spatial information. In this work, we provide new insight to the relationships among regional mutual information, regional probability distribution functions (PDFs) and global PDFs, and propose a novel nonrigid registration scheme with spatially weighted global probability distribution function (SWGPDF). Similarity measures based on SWGPDF (SWGPDFSM) are constructed. Three different spatial sub-region division methods are compared: the equally spaced sub-region (ESSR), the local binary pattern sub-region (LBPSR) and the gradient sub-region (GSR). The registration scheme applies B-spline based free form deformations (FFDs) as the transformation model. A Parzen window and linear interpolation are used to construct histograms. The SWGPDFSM registration scheme with ESSR space division is compared with the traditional global mutual information (gMI), the traditional global normalized mutual information (gNMI), regional mutual information and the SWGPDFSM with LBPSR or GSR space division. The test results show that SWGPDFSM scheme with ESSR space division outperforms the other schemes for elastically aligning images in the presence of big geometrical transformations, bias fields and illumination changes.