Normal Fans of Polyhedral Convex Sets

The normal fan of a polyhedral convex set in ? ⁿ is the collection of its normal cones. The structure of the normal fan reflects the geometry of that set. This paper reviews and studies properties about the normal fan. In particular, it investigates situations in which the normal fan of a polyhedral convex set refines, or is a subfan of, that of another set. It then applies these techniques in several examples. One of these concerns the face structure and normal manifold of the critical cone of a polyhedral convex set associated with a point in ? ⁿ . Another concerns how perturbation of the right hand side of the linear constraints defining such a set affects the normal fan and the face structure.     

Simultaneous determination of five coumarins in Angelicae dahuricae Radix by HPLC/UV and LC‐ESI‐MS/MS

Rapid, simple and reliable HPLC/UV and LC‐ESI‐MS/MS methods for the simultaneous determination of five active coumarins of Angelicae dahuricae Radix, byakangelicol (1), oxypeucedanin (2), imperatorin (3), phellopterin (4) and isoimperatorin (5) were developed and validated. The separation condition for HPLC/UV was optimized using a Develosil RPAQUEOUS C₃₀ column using 70% acetonitrile in water as the mobile phase. This HPLC/UV method was successful for providing the baseline separation of the five coumarins with no interfering peaks detected in the 70% ethanol extract of Angelicae dahuricae Radix. The specific determination of the five coumarins was also accomplished by a triple quadrupole tandem mass spectrometer equipped with an electrospray ionization source (LC‐ESI‐MS/MS). Multiple reaction monitoring (MRM) in the positive mode was used to enhance the selectivity of detection. The LC‐ESI‐MS/MS methods were successfully applied for the determination of the five major coumarins in Angelicae dahuricae Radix. These HPLC/UV and LC‐ESI‐MS/MS methods were validated in terms of recovery, linearity, accuracy and precision (intra‐ and inter‐day validation). Taken together, the shorter analysis time involved makes these HPLC/UV and LC‐ESI‐MS/MS methods valuable for the commercial quality control of Angelicae dahuricae Radix extracts and its pharmaceutical preparations. Copyright © 2009 John Wiley & Sons, Ltd.     

一类具有阶段结构和时滞的非自治捕食系统

本文研究一类具有阶段结构和时滞的非自治捕食系统解的渐近性质 ,在适当条件下 ,得到系统是持续生存的且全局渐近稳定的     

Half‐titanocene complexes bearing dianionic 6‐benzimidazolylpyridyl‐2‐carboximidate ligands: Synthesis,characterization, and their ethylene polymerization

6‐Benzimidazolylpyridyl‐2‐carboximidic half‐titanocene complexes, Cp′TiLCl (Cp′ = C₅H₅, MeC₅H₄, C₅Me₅, L = 6‐benzimidazolylpyridine‐2‐carboxylimidic, C1–C13 ), were synthesized and characterized along with single‐crystal X‐ray diffraction. The half‐titanocene chlorides containing substituted cyclopentadienyl groups, especially pentamethylcyclopentadienyl groups were more stable, while those without substituents on the cyclopentadienyl groups were easily transformed into their dimeric oxo‐bridged complexes, (CpTiL)₂O ( C14 and C15 ). In the presence of excessive amounts of methylaluminoxane (MAO) or modified methylaluminoxane (MMAO), all half‐titanocene complexes showed high catalytic activities for ethylene polymerization. The substituents on the Cp groups affected the catalytic behaviors of the complexes significantly, with less substituents favoring increased activities and higher molecular weights of the resultant polyethylenes. Effects of reaction conditions on catalytic behaviors were systematically investigated with catalytic systems of mononuclear C1 and dimeric C14 . With C1 /MAO, large MAO amount significantly increases the catalytic activity, while the temperature only has a slight effect on the productivity. In the case of C14 /MAO catalytic system, temperature above 60 °C and Al/Ti value higher than 5000 were necessary to observe good catalytic activities. In both systems, higher reaction temperature and low cocatalyst amount gave the polyethylenes with higher molecular weights. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3396–3410, 2008     

Phase and shape controlling of MnS nanocrystals in the solvothermal process

MnS nanocrystals with different phases and shapes were prepared through solvothermal synthesis. The products were characterized by X-ray diffraction (XRD), transmission electron microscope (TEM), UV–vis absorption and photoluminescence (PL) spectra. The solvent and reaction time played an important role in controlling the phase and shape of MnS nanocrystals. The possible mechanism of the shape evolution was investigated, which revealed that the crystal growth along the unique c axis of γ-MnS resulted in the rod-like MnS at the primary period, and the tetrahedral crystal seed of β-MnS with zincblende structure resulted in the interlinking of MnS rods, so the zigzag and three-branched and palm-like MnS appeared; with increasing reactive time the thermodynamically stable spherical α-MnS was favored through the Ostwald ripening process. The PL results showed that the intensity of γ-MnS was much weaker than that of α-MnS, and the trap state emissions of γ-MnS at 470 and 482 nm, respectively, disappeared, which might be ascribed to the difference of the shapes between the sphere and the rod or branch.     

超导芯截面形状对Bi-2223/Ag带Jc的影响

磁光图像显示Ｂｉ－２２２３／Ａｇ带材中单根超导芯的宽面两侧边缘分布有较大的超导电流密度，Ｂｉ－２２２３单根超导芯的横截面是纺锤形的，单位宽度上的横截面面积之比与电流密度在横截面上不同部分的分布之比相当，高的电流密度在单根超导芯两则的分布可能是由单芯横截面的形状引起的。     

Material characterization for electroconvection

We report a set of material characterizations on the nematic mixture Mischung V . With these measurements, as well as previously known results, Mischung V becomes the second nematic liquid crystal possessing a complete set of known physical parameters relevant for electroconvection, enabling quantitative comparison with theoretical predictions to be made. Additionally, we have identified a stable dopant which induces in Mischung V the electrical conductivity necessary for observing the conduction regime of electroconvection. Mischung V is thus validated as a suitable substitute for materials that have traditionally been chosen for these types of experiments. However, Mischung V does not present the same experimental difficulties as traditional materials.