Cu-catalyzed hydroxycyclopropanol ring-opening cyclization to tetrahydrofurans and tetrahydropyrans: short total syntheses of hyperiones

Tetrahydrofurans (THFs) and tetrahydropyrans (THPs) are important core scaffolds frequently found in many molecules of medicinal importance. Herein, we report a novel copper-catalyzed hydroxycyclopropanol ring-opening cyclization methodology to synthesize di- or tri-substituted THFs and THPs. In this reaction, a strained C–C bond was cleaved and a new Csp³–O bond was formed to produce the aforementioned O-heterocycles. The new THF synthesis features a broad substrate scope, scalability, and good functional-group tolerability. It enabled us to complete the shortest enantioselective syntheses of hyperiones A and B (3 and 4 steps, respectively), which is significantly shorter than the previously reported two total syntheses (≥10 steps).

A novel Cu-catalyzed hydroxycyclopropanol ring-opening cyclization was developed to synthesize substituted tetrahydrofuran/tetrahydropyran molecules including two norlignan natural products hyperiones A and B.     

蒙旦树脂化学组成的研究

采用阴离子交换色谱和硅胶－氧化铝柱色谱对云南寻甸蒙旦树脂（ＸＤＳＺ）、潦浒蒙旦树脂（ＬＨＳＺ）、昭通蒙旦树脂（ＺＴＳＺ）和吉林舒兰蒙旦树脂（ＳＬＳＺ）进行了族组分的分离。树脂游离酸，树脂结合酸，树脂烃和树脂醇在各树脂中的百分含量分别为ＸＤＳＺ１１．８６，８．７６，１２．３０，４５．９９；ＬＨＳＺ１５．８９，１３．９１，４．９０，４５．９９；ＳＬＳＺ２５．４６，８．０７，１７．４０，３６．２２；ＺＴ     

Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature

The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in Rⁿ. They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces. In particular, they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume, which can be seen as the higher-dimensional generalization of the pseudo-sphere.     

Limit cycle analysis of a class of strongly nonlinear oscillation equations

The limit cycle of a class of strongly nonlinear oscillation equations of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqadwhagaWaaiabgUcaRmXvP5wqonvsaeHbbjxAHXgiofMCY92D% aGqbciab-DgaNjab-HcaOiaadwhacqWFPaqkcqWF9aqpcqaH1oqzca% WGMbGaaiikaiaadwhacaGGSaGabmyDayaacaGaaiykaaaa!50B8!\[\ddot u + g(u) = \varepsilon f(u,\dot u)\] is investigated by means of a modified version of the KBM method, where is a positive small parameter. The advantage of our method is its straightforwardness and effectiveness, which is suitable for the above equation, where g(u) need not be restricted to an odd function of u, provided that the reduced equation, corresponding to =0, has a periodic solution. A specific example is presented to demonstrate the validity and accuracy of our 09 method by comparing our results with numerical ones, which are in good agreement with each other even for relatively large .