固相萃取-气相色谱法测定甲醇制烯烃副产汽油及甲醇制汽油产物中的含氧化合物

采用纯硅胶柱固相萃取技术对甲醇制烯烃副产汽油或甲醇制汽油产物进行预处理,将产物中的含氧化合物与烃类进行色谱分离,采用质谱鉴定产物中的含氧化合物。使用标准溶液优化纯硅胶小柱的洗脱条件,比较预处理方法的回收率,考察预处理方法的重复性。结果表明,标准溶液的各含氧化合物组分回收率为87.7%~95.3%。采用气相色谱-火焰离子化检测器(GC-FID)通过内标法对实际样品中除甲醇和乙醇外的含氧化合物进行定量分析,使用丁酮、叔戊醇、戊酮和己酮的响应因子作为同碳数醛、酮、醇的FID响应因子,定量甲醇制烯烃副产汽油和甲醇制汽油产物中的含氧化合物。对于甲醇和乙醇,采用GC-MS分析提取特征离子用外标法定量。结果表明,甲醇制烯烃副产汽油和甲醇制汽油产物中的含氧化合物以酮类、醛类为主,并有少量的醇类。     

[4 1]及[3 2]会聚式四氢呋喃环合成策略在天然产物全合成中的应用进展

四氢呋喃环广泛存在于具有生物活性的天然产物结构当中,立体选择性地构筑四氢呋喃环往往成为这些天然产物全合成研究中的关键。本文归纳了已有全合成报道中的四氢呋喃环成环策略,以实例展示了其中的会聚式合成策略在近年的发展。相比于直线型的分子内关环策略,以[4+1]、[3+2]为代表的会聚式四氢呋喃关环策略往往能够使全合成的整体路线更加简洁高效,更符合全合成研究领域的发展趋势。     

Exact and approximation product solutions form of heat equation with nonlocal boundary conditions using Ritz–Galerkin method with Bernoulli polynomials basis

In this article, a new method is introduced for finding the exact solution of the product form of parabolic equation with nonlocal boundary conditions. Approximation solution of the present problem is implemented by the Ritz–Galerkin method in Bernoulli polynomials basis. The properties of Bernoulli polynomials are first presented, then Ritz–Galerkin method in Bernoulli polynomials is used to reduce the given differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the techniques presented in this article for finding the exact and approximation solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1143–1158, 2017     

Further results on generalized inverses of tensors via the Einstein product

The notion of the Moore–Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate on this theory by producing a few characterizations of different generalized inverses of tensors. A new method to compute the Moore–Penrose inverse of tensors is proposed. Reverse order laws for several generalized inverses of tensors are also presented. In addition to these, we discuss general solutions of multilinear systems of tensors using such theory.     

两类图的(d,1)-全标号

主要讨论了W_n与C_m的笛卡尔积和均衡完全r-部图K_r(n)的(d,1)-全标号,并得出了(d,1)-全数λ_d~T(W_n□C_m)和λ_d~T(K_(r(n)))的确切值.     

圈积的词长度公式

利用Fordham的技巧证明了圈积群HιZ的一个词长度公式,其中H是一个有限生成群,Z是整数群.     

Site-selective Csp3-H aryloxylation of natural product Tanshinone IIA and its analogues

A novel catalyst-free Csp³-H aryloxylation approach allowing for rapid installation of a wide range of aryloxyl groups regioselectively at the C-4 position of Tanshinone IIA under simple and mild conditions was developed. This unique protocol exhibited atom-/step-economy, low cost, high efficiency and robust functional-group tolerance, which will greatly facilitate to diversify the A-ring of the bioactive natural product.     

Total synthesis of chrysamide B

We report an efficient synthesis of the dimeric trans-epoxyamide chrysamide B, recently isolated from the deep-sea-derived fungus Penicillium chrysogenum SCSIO41001. Our synthetic strategy exploits a convergent approach using solid-phase peptide synthesis for the piperazine core and a Sharpless-Katsuki epoxidation to prepare the chiral epoxyacid. The double amidation final step provides chrysamide B that was thoroughly characterized with all spectra identical to those of the natural sample. The approach was devised to facilitate the preparation of a library of analogs of chrysamide B.     

Toll number of the Cartesian and the lexicographic product of graphs

Toll convexity is a variation of the so-called interval convexity. A tolled walk $T$ between two non-adjacent vertices $u$ and $v$ in a graph $G$ is a walk, in which $u$ is adjacent only to the second vertex of $T$ and $v$ is adjacent only to the second-to-last vertex of $T$. A toll interval between $u,v\in V\left(G\right)$ is a set $T_G(u,v)=\{x\in V\left(G\right):x\text{ lies on a tolled walk between }u\text{ and }v\}$. A set $S?V\left(G\right)$ is toll convex, if $T_G(u,v)?S$ for all $u,v\in S$. A toll closure of a set $S?V\left(G\right)$ is the union of toll intervals between all pairs of vertices from $S$. The size of a smallest set $S$ whose toll closure is the whole vertex set is called a toll number of a graph $G$, $tn\left(G\right)$. The first part of the paper reinvestigates the characterization of convex sets in the Cartesian product of two graphs. It is proved that the toll number of the Cartesian product of two graphs equals 2. In the second part, the toll number of the lexicographic product of two graphs is studied. It is shown that if $H$ is not isomorphic to a complete graph, $tn(G°H)\le 3?tn\left(G\right)$. We give some necessary and sufficient conditions for $tn(G°H)=3?tn\left(G\right)$. Moreover, if $G$ has at least two extreme vertices, a complete characterization is given. Furthermore, graphs with $tn(G°H)=2$ are characterized. Finally, the formula for $tn(G°H)$ is given — it is described in terms of the so-called toll-dominating triples or, if $H$ is complete, toll-dominating pairs.