Nested hierarchies in planar graphs

We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph G and defines a unique hierarchy. We demonstrate that G is the union of a set of special subgraphs, named ‘bubbles’, that are themselves maximal planar graphs. The graph G is retrieved by connecting these bubbles in a tree structure where neighboring bubbles are joined together by a 3-clique. Bubbles naturally provide the subdivision of G into communities and the tree structure defines the hierarchical relations between these communities.     

带正则*-断面的正则半群

本文给出了带正则*-断面的正则半群的若干性质,获得了带拟理想正则*-断面的正则半群的一个构造方法.利用这一构造定理,考虑了这类半群上的同余.     

Generalized Cheeger-Gromoll metrics and the Hopf map

We show that there exists a family of Riemannian metrics on the tangent bundle of a two-sphere, which induces metrics of constant curvature on its unit tangent bundle. In other words, given such a metric on the tangent bundle of a two-sphere, the Hopf map is identified with a Riemannian submersion from the universal covering space of the unit tangent bundle, equipped with the induced metric, onto the two-sphere. A hyperbolic counterpart dealing with the tangent bundle of a hyperbolic plane is also presented.     

湍流运动论中的化学反应速率扰动

在分子与分子之间发生碰撞时,如果分子的动能足够大,当超过一定的阈值E时,分子碰撞就会发生化学反应.然而气体分子化学反应速率是受到一定因素影响的,诸如分子数密度n、温度T以及速度V.日本学者Sagara于上世纪70年代曾对分子数密度n和温度T对反应速率的变化做了深入的探究.主要是在此基础上利用二粒碰撞机理论对速度以及温度和速度的共同作用来研究反应速率的变化情况.     

水资源短缺风险因子的筛选模型

水资源短缺评价首先需要确定指标体系,投影寻踪模型与灰色关联度法相结合,可以有效地筛选出水资源短缺风险因子,为进一步进行风险评价奠定了基础,同时也为制定风险的防范措施和对策提供了理论依据.综合应用这两种模型,对北京市2001～2009年的水资源短缺风险进行研究,结果表明:降水量、日照时数、雨日数、单位GDP污水排放量、人均GDP、工业总产值占有率、污水处理率和水循环使用率这8个指标是北京市水资源短缺的主要风险因子.     

New scenarios of protein folding can occur on the ribosome

Identifying and understanding the differences between protein folding in bulk solution and in the cell is a crucial challenge facing biology. Using Langevin dynamics, we have simulated intact ribosomes containing five different nascent chains arrested at different stages of their synthesis such that each nascent chain can fold and unfold at or near the exit tunnel vestibule. We find that the native state is destabilized close to the ribosome surface due to an increase in unfolded state entropy and a decrease in native state entropy; the former arises because the unfolded ensemble tends to behave as an expanded random coil near the ribosome and a semicompact globule in bulk solution. In addition, the unfolded ensemble of the nascent chain adopts a highly anisotropic shape near the ribosome surface and the cooperativity of the folding-unfolding transition is decreased due to the appearance of partially folded structures that are not populated in bulk solution. The results show, in light of these effects, that with increasing nascent chain length folding rates increase in a linear manner and unfolding rates decrease, with larger and topologically more complex folds being the most highly perturbed by the ribosome. Analysis of folding trajectories, initiated by temperature quench, reveals the transition state ensemble is driven toward compaction and greater native-like structure by interactions with the ribosome surface and exit vestibule. Furthermore, the diversity of folding pathways decreases and the probability increases of initiating folding via the N-terminus on the ribosome. We show that all of these findings are equally applicable to the situation in which protein folding occurs during continuous (non-arrested) translation provided that the time scales of folding and unfolding are much faster than the time scale of monomer addition to the growing nascent chain, which results in a quasi-equilibrium process. These substantial ribosome-induced perturbations to almost all aspects of protein folding indicate that folding scenarios that are distinct from those of bulk solution can occur on the ribosome.     

A successful chemical strategy to induce oligothiophene self-assembly into fibers with tunable shape and function

Functional supramolecular architectures for bottom-up organic nano- and microtechnology are a high priority research topic. We discovered a new recognition algorithm, resulting from the combination of thioalkyl substituents and head-to-head regiochemistry of substitution, to induce the spontaneous self-assembly of sulfur overrich octathiophenes into supramolecular crystalline fibers combining high charge mobility and intense fluorescence. The fibers were grown on various types of surfaces either as superhelices or straight rods depending on molecular structure. Helical fibers directly grown on a field effect transistor displayed efficient charge mobility and intrinsic 'memory effect'. Despite the fact that the oligomers did not have chirality centers, one type of hand-helicity was always predominant in helical fibers, due to the interplay of molecular atropisomerism and supramolecular helicity induced by terminal substituents. Finally, we found that the new sulfur overrich oligothiophenes can easily be prepared in high yields through ultrasound and microwave assistance in green conditions.     

Pyranoside phosphite-oxazoline ligands for the highly versatile and enantioselective ir-catalyzed hydrogenation of minimally functionalized olefins. A combined theoretical and experimental study

A modular set of phosphite-oxazoline (P,N) ligands has been applied to the title reaction. Excellent ligands have been identified for a range of substrates, including previously challenging terminally disubstituted olefins, where we now have reached enantioselectivities of 99% for a range of substrates. The selectivity is best for minimally functionalized substrates with at least a moderate size difference between geminal groups. A DFT study has allowed identification of the preferred pathway. Computational prediction of enantioselectivities gave very good accuracy.     

Spherical Periodic Mesoporous Organosilicas Bearing Camphorsulfonamide Substructures for HPLC

New mesoporous organic?Cinorganic spheres were prepared by one step co-condensation of trialkoxysilylated camphorsulfonamide (CSA) and 1,2-bis(triethoxysilyl)ethane (BTSE) using octadecyltrimethylammonium chloride (C₁₈TMACl) as template and ethanol as co-solvent in basic medium. The materials have been characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), powder X-ray diffraction (XRD), nitrogen sorption measurement, diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and elemental analysis (EA). Then the mesoporous organic?Cinorganic spheres were demonstrated to be novel packing materials for potential application in the normal-phase high performance liquid chromatography (HPLC).