Asymmetric Total Synthesis of (+)‐Ryanodol and (+)‐Ryanodine

(+)‐Ryanodine ( 1 ) is the ester derivative of 1H‐pyrrole‐2‐carboxylic acid and the complex terpenoid (+)‐ryanodol ( 2 ), which possesses eleven contiguous stereogenic centers on the ABCDE‐ring system. Compound 1 is known to be a potent modulator of intracellular calcium release channels, whereas the activity of 2 is significantly weaker. To chemically construct 1 , the multiple oxygen functional groups must be installed on the fused pentacycle in stereoselective fashions and the extremely hindered C3‐hydroxy group must be acylated in a site‐selective manner. First, the total synthesis of 2 was accomplished by introducing the five stereocenters from the previously prepared enantiopure ABDE‐ring 7 . Stereoselective construction of the C3‐secondary, C2‐ and C6‐tertiary alcohols was achieved by three nucleophilic reactions. The C9‐ and C10‐trisubstituted carbon centers were regio‐ and stereoselectively introduced by hydroboration/oxidation of the six‐membered C‐ring, which was formed by the ring‐closing metathesis reaction. Direct esterification of the C3‐alcohol with pyrrole‐2‐carboxylic acid proved unsuccessful; therefore, we developed a new, two‐step protocol for attachment of the pyrrole moiety. The C3‐hydroxy group was first converted into the less sterically cumbersome glycine ester, which was then transformed into the pyrrole ring through condensation with 1,3‐bis(dimethylamino)allylium tetrafluoroborate. This procedure resulted in the first total synthesis of 1 .     

图$P_m\times P_n, P_m\times C_n$ 和C_m\times C_n$}的邻点可区别全色数的注记

设 $G$ 是一个简单图. 设$f$是从$V(G) \cup E(G)$到 $\{1, 2,\ldots, k\}$的一个映射.对任意的 $v\in V(G)$, 设$C_f(v)=\{f(v)\}\cup \{f (vw)|w\in V(G),vw\in E(G)\}$ . 如果 $f$ 是一个 $k$-正常全染色, 且对 $u, v\in V(G),uv\in E(G)$, 有 $C_f(u)\neq C_f(v)$, 那么称 $f$ 为$k$-邻点可区别全染色 (简记为$k$-$AVDTC$). 设     

Hamming极小距离最小上界的研究

Hamming极小距离在扩散码、纠错码、检错码等领域有广泛的应用. 本文提出了 F2、 Fq上矩阵总行间距、平均行间距等概念 , 给出并证明了总行间距、极小行间距的最小上界定理 ,在此基础上得到了 Vn( F 2 )、 Vn( Fq) 中 Hamming极小距离的最小上界 , 同时给出了多比特扩散码中参数 d的上确界、线性码 ( n, k) 是最优码的一个必要条件.     

On the Harris Recurrence of Iterated Random Lipschitz Functions and Related Convergence Rate Results

A result by Elton⁽⁶⁾ states that an iterated function system