Towards a quaternionic function theory linked with the Lamé's wave functions

Over the past few years, considerable attention has been given to the role played by the Lamé's Wave Functions (LWFs) in various problems of mathematical physics and mechanics. The LWFs arise via the method of separation of variables for the wave equation in ellipsoidal coordinates. The present paper introduces the Lamé's Quaternionic Wave Functions (LQWFs), which extend the LWFs to a non‐commutative framework. We show that the theory of the LQWFs is determined by the Moisil‐Theodorescu type operator with quaternionic variable coefficients. As a result, we explain the connections between the solutions of the Lamé's wave equation, on one hand, and the quaternionic hyperholomorphic and anti‐hyperholomorphic functions on the other. We establish analogues of the basic integral formulas of complex analysis such as Borel‐Pompeiu's, Cauchy's, and so on, for this version of quaternionic function theory. We further obtain analogues of the boundary value properties of the LQWFs such as Sokhotski‐Plemelj formulae, the ‐hyperholomorphic extension of a given Hölder function and on the square of the singular integral operator. We address all the text mentioned earlier and explore some basic facts of the arising quaternionic function theory. We conclude the paper showing that the spherical, prolate, and oblate spheroidal quaternionic wave functions can be generated as particular cases of the LQWFs. Copyright © 2015 John Wiley & Sons, Ltd.     

(PtAuPt)HN/GC的制备及对甲酸氧化的电催化性能

以Se溶胶为模板,合成了多层核壳结构的Se@Pt@Au@Pt实心纳米粒子;采用化学与电化学相结合的除硒方法制得了(PtAuPt)HN/GC,并表征了(PtAuPt-Se)HN的表面形貌、结构与组成;以甲酸为探针分子,比较了(PtAuPt)HN/GC和Pt/C/GC对甲酸氧化的电催化行为,发现(PtAuPt)HN/GC催化甲酸氧化只有1个氧化峰,峰电位和峰电流分别约为0.35V和1.22mA/cm2,而Pt/C/GC则有2个氧化峰,在0.35V时所对应的电流密度仅约为0.30mA/cm2,前者在该电位时的电流密度是后者的4倍;在0.30mA/cm2的电流密度下,(PtAuPt)HN/GC对应的电极电位为0.01V,比Pt/C/GC负移了340mV;在600s时的计时电流分别为0.06和0.02mA/cm2.(PtAuPt)HN对甲酸氧化的电催化活性不但比Pt/C高,而且具有一定的抗CO中毒性能.     

Preparation and Photocatalytic Activity of Ce,H3PW12O40 co-doped TiO2 Hollow Fibers

A series of Ce, H3PW12O40 co-doped TiO2 hollow fibers photocatalysts have been prepared by sol-gel method using ammonium ceric nitrate, H3PW12O40 and tetrabutyltitanate as precursors and cotton fibers as template, followed by calcination at 500 ℃ in N2 atmosphere for 2 h. Scanning electron microscopy, X-ray diffraction, nitrogen adsorption-desorption mea- surements, and UV-Vis spectroscopy are employed to characterize the morphology, crystal structure, surface structure, and optical absorption properties of the samples. The photo- catalytic performance of the samples has been studied by photodegradation phenol in water under UV and visible light irradiation. The results show that the TiO2 fiber materials have hollow structures, and the co-doped TiO2 hollow fibers exhibit higher photocatalytic activities for the degradation of phenol than un-doped, single-doped TiO2 hollow fibers under UV and visible light. In addition, the recyclability of co-doped TiO2 fibers is also confirmed that the TiO2 fiber retains ca. 90% of its activity after being used four times. It is shown that the co-doped TiO2 fibers can be activated by visible light and may be potentially applied to the treatment of water contaminated by organic pollutants. The synergistic effect of Ce and H3PW12O40 co-doping plays an important role in improving the photocatalytic activity.     

Formation of Hexagonally Packed Hollow Hoops and Morphology Transition in RAFT Ethanol Dispersion Polymerization

Similar to the traditional self‐assembly strategy, polymerization induced self‐assembly and reorganization (PISR) can produce a myriad of polymeric morphologies through morphology transitions. Besides the chain length ratio (R) of the hydrophobic to the hydrophilic blocks, the chain mobility in the intermediate nano‐objects, which is a requisite for morphology transition, is a determining factor in the formation of the final morphology. Although various morphologies have been fabricated, hexagonally packed hollow hoops (HHHs) with highly ordered internal structure have not, to the best of our knowledge, been prepared by PISR. In this article, the fabrication of HHHs through morphology transition from large compound vesicles to HHHs is reported. HHHs with highly regular internal structure may have significance in theoretical research and practical applications of nanomaterials.

     

石墨烯包覆天然球形石墨作为锂离子电池的负极材料，是否需要乙炔黑导电剂？

我们通过包覆炭化的方法制备得到了石墨烯包覆的天然球形石墨(G/SG)材料,并使用扫描电子显微镜、X射线衍射仪以及多种电化学测试手段考察了不同石墨烯含量的复合材料的形貌结构及电化学性能。我们发现,在不添加乙炔黑(AB)的情况下,G/SG复合材料表现出较高的首次库伦效率,很好的循环稳定性和高倍率性能。当石墨烯包覆量为1%时,材料50次循环后的可逆容量可与添加10%AB的天然石墨电极(SG)等同;当石墨烯包覆量为2.5%时,材料的比容量完全高于添加10%AB的石墨电极。材料电化学性能的改善归因于石墨烯的包覆。一方面,石墨烯的柔软可变性可以保证天然石墨颗粒在充放电过程中的结构完整性,从而有效改善材料的循环稳定性;另一方面,石墨烯的存在提高了电极的导电性,促进更好导电网络的形成。因此,石墨烯包覆天然球形石墨材料中,石墨烯不仅是活性物质,也发挥导电剂的作用。当添加5%的乙炔黑时,在50 mA·g^-1电流循环50次后,5%G/SG电极的可逆容量从381.1 mAh·g^-1提高到404.5 mAh·g^-1,在1 A·g^-1电流时可逆容量从82.5 mAh·g^-1提高到101.9 mAh·g^-1,这表明G/SG电极仍然需要乙炔黑导电剂。乙炔黑颗粒填充在复合材料的空隙中,通过点接触的形式连接到G/SG颗粒,与石墨烯协同作用形成了更加有效的导电网络。尽管石墨烯包覆和乙炔黑添加对天然石墨电极具有积极的影响,例如增加了天然石墨电极的导电性和储锂性能(包括可逆容量,倍率性能和循环性能),但随着石墨烯或乙炔黑的增加,电极密度通常会降低。因此,在实际应用中应考虑石墨负极材料的质量和体积容量的平衡。这些结果对天然石墨的进一步商业应用具有重要意义。我们的工作为天然石墨电极在锂电池中的电化学行为提供了一种新的认识,并且有助于制备更高性能的负极材料。     

MRI相关定量参数在肩峰下撞击综合征诊断中的价值及与肩关节功能、治疗效果的关系

为分析MRI相关定量参数对肩峰下撞击综合征(SIS)的诊断价值,本研究将56例SIS患者设为SIS组,同期56例健康体检者设为对照组,对比了两组对象的一般资料、肩关节功能评分(Constant评分)及MRI相关定量参数水平,探讨了MRI定量参数与Constant评分、SIS发病相关影响因素、治疗效果的关系及对SIS的诊断价值。结果显示SIS组Constant评分、最短肩肱间距低于对照组,肩峰指数、肩锁关节骨赘高度高于对照组,且SIS组治疗有效患者肩峰指数、肩锁关节骨赘高度低于无效患者,最短肩肱间距高于无效患者(P<0.05);SIS患者肩峰指数、肩锁关节骨赘高度与Constant评分呈负相关,而最短肩肱间距与其呈正相关(P<0.05);各MRI相关定量参数均为SIS发病的重要影响因素(P<0.05)。应用各MRI相关定量参数联合诊断SIS特异度为87.50%,敏感度为80.36%。由此可知MRI相关定量参数对SIS诊断价值较高,且与肩关节功能和治疗效果有关。     

一步硫/磷热处理制备空心Co9S8/CoP/C纳米复合材料及其储钠性能研究

低成本、高性能的钠离子电池有望成为代替锂离子电池的下一代核心器件.但是开发出高比容量、高倍率的钠离子电池负极材料依然是瓶颈.本文通过水热/溶剂热法制备了Co基前驱体,然后将其一步硫/磷热处理制得具有空心多孔结构的h-Co₉S₈/CoP/C纳米复合材料.通过X-射线粉末衍射(XRD)、拉曼光谱(Raman)、扫描电镜(SEM)、透射电镜(TEM)和X-射线光电子能谱(XPS)等表征以确定纳米复合物的物相以及形貌特征.当h-Co₉S₈/CoP/C作为钠离子电池负极材料时,该电极材料展示了高的比容量(561 mAh g^-1@0.1 Ag^-1)、较好的循环性能(可逆比容量200 mAh g^-1@2 Ag^-1)和倍率性能.h-Co₉S₈/CoP/C之所以显示出良好的储钠性能,主要得益于其空心多孔结构不仅提供更多的空间缓解钠在反复嵌入和脱出过程造成的体积膨胀效应,而且可以缩短离子/电荷扩散途径以加快反应动力学,此外,Co₉S₈、CoP和C独特的电子结构优势得以共同发挥.