On the conformal mappings in the unit disk fixing arbitrarily many boundary points

In this paper, we give a method of constructing conformal mappings defined in the unit disk which can fix arbitrarily many points on the unit circle.     

RABA (Reductive Alkylation By Acetone): A novel stable isotope labeling approach for quantitative proteomics

Quantitative proteomics is challenging and various stable isotope based approaches have been developed to meet the challenge. Hereby we describe a simple, efficient, reliable, and inexpensive method named reductive alkylation by acetone (RABA) to introduce stable isotopes to peptides for quantitative analysis. The RABA method leads to alkylation of N-terminal and lysine amino groups with isopropyl moiety. Using unlabeled (d₀) and deuterium labeled (d₆) acetone, a 6 Da mass split is introduced to each isopropyl modification between the light and heavy isotope labeled peptides, which is ideally suited for quantitative analysis. The reaction specificity, stoichiometry, labeling efficiency, and linear range of the RABA method have been thoroughly evaluated in this study using standard peptides, tryptic digest of proteins, as well as human cell lysate. Reliable quantitative results have been consistently obtained in all experiments. We also applied the RABA method to quantitative analysis of proteins in spinal cords of transgenic mouse models of amyotrophic lateral sclerosis. Highly homologous proteins (transgenic human SOD1 and endogenous mouse SOD1) were distinguished and quantified using the method developed in this study. In addition, the quantitative results using the RABA approach were independently validated by Western blot.     

Novel ring-cleaving reaction of 4-nitro-1,1,2,2,9,9,10,10-octafluoro[2.2]paracyclophane with nucleophiles

When 4-nitro-AF4 is treated with nucleophiles such as alkoxides and cyanide, a novel ring opening, cyclophane destroying reaction is observed whereby, via an S_NAr mechanism, the nucleophile attacks the bridgehead aryl carbon vicinal to the nitro group with subsequent aryl-CF₂ bond cleavage.     

双圈连通图的L(2,1)-labelling

给定图G,G的一个L(2,1)-labelling是指一个映射f:V(G)→{0,1,2,…},满足:当dG(u,v)=1时,f(u)-f(v)≥2;当dG(u,v)=2时,f(u)-f(v)≥1.如果G的一个L(2,1)-labelling的像集合中没有元素超过k,则称之为一个k-L(2,1)-labelling.G的L(2,1)-labelling数记作l(G),是指使得G存在k-L(2,1)-labelling的最小整数k.如果G的一个L(2,1)-labelling中的像元素是连续的,则称之为一个no-holeL(2,1)-labelling.本文证明了对每个双圈连通图G,l(G)=△ 1或△ 2.这个工作推广了[1]中的一个结果.此外,我们还给出了双圈连通图的no-hole L(2,1)-labelling的存在性.     

湿有效能量预报暴雨的动力分析

根据7个例子的对比分析表明:湿有效能量对预报暴雨具有较好的指示性,但在某些条件下湿有效能量在有无暴雨发生两者上并无明显差别。对暴雨和无暴雨个例的动力条件分析表明:(1)有暴雨时,在杭州地区为一个相对辐散区(300—900百帕),并伴有较强的上升运动,无暴雨时则为相对辐合区;(2)暴雨时高空有一支强的急流,暴雨区位于高空发散流场和急流中心的入口区右侧。(3)稳定度大小两者也有明显差异。分析结果对业务预报有一定参考价值。     

Path Decomposition of Graphs with Given Path Length

A path decomposition of a graph G is a list of paths such that each edge appears in exactly onepath in the list.G is said to admit a {P_l}-decomposition if G can be decomposed into some copies of P_l,whereP_l is a path of length l-1.Similarly,G is said to admit a {P_l,P_k}=decomposition if G can be decomposed intosome copies of P_l or P_k.An k-cycle,denoted by C_k,is a cycle with k vertices.An odd tree is a tree of which allvertices have odd degree.In this paper,it is shown that a connected graph G admits a {P_3,P_4}-decompositionif and only if G is neither a 3-cycle nor an odd tree.This result includes the related result of Yan,Xu andMutu.Moreover,two polynomial algorithms are given to find {P_3}-decomposition and {P_3,P_4}-decompositionof graphs,respectively.Hence,{P_3}-decomposition problem and {P_3,P_4}-decomposition problem of graphs aresolved completely.     

A theoretical kinetics study on low-temperature oxidation of n-C4H9 radicals

The low-temperature oxidation mechanism of n?butyl radicals (n-C₄H₉) has been investigated by high level quantum chemical calculations coupled with the Rice–Ramsperger–Kassel–Marcus/Master Equation (RRKM/ME) theory. The potential energy surfaces (PES) were explored at the QCISD(T)/CBS//B3LYP/6-311++G(d,p) level. The temperature- and pressure-dependent rate constants were computed and fitted in modified Arrhenius parameters. The major reaction channels were discussed to more deeply understand the competing relationships between chain branching, chain propagation and termination reactions. The results show that the 1,5 H-shift reaction is more competitive than the 1,6 H-shift and 1,4 H-shift for isomerization reactions of n?butyl peroxy radicals, and the concerted HO₂ elimination channel to form butene becomes more important at high temperatures. Furthermore, based on our calculations, a revised kinetic model was developed to describe n-butane oxidation. Good consistency between model predictions and experimental data was shown. This study enhances our understanding of the combustion mechanism of n-butane and can be used as a reliable reference for mechanistic understanding of larger alkanes.