A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs

After a careful consideration of some of the well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs, we were able to deduce a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coe?cients of its associated double-class algebra can be written in terms of zonal spherical functions. This is a generalization of the Frobenius formula which expresses the structure coe?cients of the center of a finite group algebra in terms of irreducible characters.     

Green's function approach to study the propagation of SH‐wave in piezoelectric layer influenced by a point source

Green's function technique serves as a powerful tool to find the particle displacements due to SH‐wave propagation in layer of a shape different from the space between two parallel planes. Therefore, the present paper undertook to study the propagation of SH‐wave in a transversely isotropic piezoelectric layer under the influence of a point source and overlying a heterogeneous substrate using Green's function technique. The coupled electromechanical field equations are solved with the aid of Green's function technique. Expression for displacements in both layer and substrate, scalar potential and finally the dispersion relation is obtained analytically for the case when wave propagates along the direction of layering. Numerical computations are carried out and demonstrated with the aid of graphs for six different piezoelectric materials namely PZT‐5H ceramics, Barium titanate (BaTiO₃) ceramics, Silicon dioxide (SiO₂) glass, Borosilicate glass, Cobalt Iron Oxide (CoFe₂O₄), and Aluminum Nitride (AlN). The effects of heterogeneity, piezoelectric and dielectric constants on the dispersion curve are highlighted. Moreover, comparative study is carried out taking the phase velocity for different piezoelectric materials on one hand and isotropic case on the other. Dispersion relation is reduced to well‐known classical Love wave equation with a view to illuminate the authenticity of problem. Copyright © 2017 John Wiley & Sons, Ltd.     

Random points in halfspheres

A random spherical polytope P_n in a spherically convex set as considered here is the spherical convex hull of n independent, uniformly distributed random points in K. The behaviour of P_n for a spherically convex set K contained in an open halfsphere is quite similar to that of a similarly generated random convex polytope in a Euclidean space, but the case when K is a halfsphere is different. This is what we investigate here, establishing the asymptotic behaviour, as n tends to infinity, of the expectation of several characteristics of P_n, such as facet and vertex number, volume and surface area. For the Hausdorff distance from the halfsphere, we obtain also some almost sure asymptotic estimates. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 3–22, 2017     

Are Nanoparticles Spherical or Quasi‐Spherical?

The geometry of quasi‐spherical nanoparticles is investigated. The combination of SEM imaging and electrochemical nano‐impact experiments is demonstrated to allow sizing and characterization of the geometry of single silver nanoparticles.     

Unique Separation Behavior of a C60 Fullerene‐Bonded Silica Monolith Prepared by an Effective Thermal Coupling Agent

Herein, we report a newly developed C₆₀ fullerene‐bonded silica monolith in a capillary with unique retention behavior due to the structure of C₆₀ fullerene. N‐Hydroxysuccinimide (NHS)‐conjugated C₆₀ fullerene was successfully synthesized by a thermal coupling agent, perfluorophenyl azide (PFPA), and assigned by spectroscopic analyses. Then, NHS‐PFPA‐C₆₀ fullerene was attached onto the surface of a silica monolith in a capillary. The capillary provided specific separation ability for polycyclic aromatic hydrocarbons in liquid chromatography by an effective π–π interaction. Furthermore, corannulene, which has a hemispherical structure, was selectively retained in the capillary based on the specific structural recognition due to the spherical C₆₀ fullerene. This is the first report revealing the spherical recognition ability by C₆₀ fullerene in liquid chromatographic separation.     

ZnS纳米球的水热法制备及其光催化性能研究

在表面活性剂十六烷基三甲基溴化铵(CTAB)的辅助下,以乙酸锌为锌源,硫脲(NH2)2CS为硫源,使用水热法通过改变反应时间,成功制备了不同粒径的ZnS球状颗粒。利用X射线衍射(XRD)、扫描电子显微镜(SEM)、X-射线能谱,高分辨透射电子显微镜(HRTEM))、紫外可见分光光谱和光致发光谱(PL)等测试手段对样品的晶体结构、形貌、光学性质进行了分析。通过对不同粒径的ZnS纳米颗粒对亚甲基蓝的光催化降解的催化活性进行了评估。实验结果表明:在表面活性剂CTAB的作用下,随着反应时间的增加,生成的ZnS晶核生长成纳米颗粒,然后ZnS纳米颗粒将进一步发生团聚从而形成平均粒径超过500nm的ZnS纳米球,但制备的ZnS产物的晶体结构均为立方纤锌矿结构。随着ZnS粒径的增加,样品的紫外吸收峰从418nm逐渐蓝移到362nm,而PL发射峰位的峰强随着粒径的增大而增强。光催化结果显示,反应12h制备的ZnS纳米球的光催化性能最佳。     

Morphology transformation of micrometre-sized giant vesicles based on physical conditions for photopolymerisation-induced self-assembly

The physical conditions to vary the morphology of vesicles formed by amphiphilic poly(methacrylic acid)-block-poly(methyl methacrylate-random-methacrylic acid) were determined for the self-assembly induced by the nitroxide-mediated photocontrolled/living radical polymerisation performed in an aqueous methanol solution. The copolymer produced micrometre-sized spherical vesicles in the solution with a 30 wt% water content. The vesicles were transformed into a film-like morphology by decreasing the water content, whereas they were changed into nanometre-sized spherical vesicles by increasing it. The concentration of the growing polymer chain also varied the morphology. Large spherical vesicles formed at a low concentration were transformed into much smaller vesicles, followed by rod-like vesicles as a result of increasing the concentration. Furthermore, the stirring speed during the polymerisation-induced self-assembly dominated the morphology. Large elliptical vesicles produced at a low stirring speed changed into spherical vesicles, but decreased the size as the speed increased.     

2-3型压电复合材料有效特性及其静水压性能的研究

压电复合材料是由至少一种压电材料与非压电材料按照一定的连通方式组合在一起而构成的具有压电效应的材料。采用均匀场理论,提出了2-3型压电复合材料的代表性体积单元,通过建立串联、并联等模型预估了压电复合材料的弹性刚度常数:C11、C12、C13、C22、C23、C33,压电常数:e31e、32e、33,介电常数:3ε3。然后用有限元方法(使用了有限元分析软件ANSYS)分析了压电复合材料的材料常数,并用有限元方法验证了均匀场理论求解2-3型压电复合材料有效特性参数的准确性。根据求得的有效特性参数进一步研究了2-3型压电复合材料的静水压性能,由于求得的静水压性能值很低,又改良了2-3型压电复合材料的模型,获得了较好的静水压性能。并将改良前后2-3型压电复合材料与3-2型压电复合材料的静水压性能进行了比较。     

战车用惯性定位定向系统的支架误差分析及补偿

战车用惯性定位定向系统由于采用双轴陀螺平台结构,不可避免地存在着支架误差,从而影响系统航向精度。应用球面三角法和方向余弦矩阵法分别推导出双轴陀螺平台的支架误差公式,发现由这两种方法推导出来的公式计算结果是一致的。最后通过数学仿真和分析,给出了支架误差与载体的姿态角之间的定量关系。根据此误差公式,对惯性定位定向系统的航向输出能够进行误差补偿,从而保证了动态条件下定位定向系统的航向输出精度。     

THREE-DIMENSIONAL INTERACTIONS OF CIRCULAR CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources: force dipoles, electric dipoles, moments, force dilatation and rotation. The circular crack includes penny-shaped crack and external circular crack and the locations and orientations of these resultant sources with respect to the crack are arbitrary. Such stress and charge sources may model defects like vacancies, foreign particles, and dislocations. Numerical results are presented at last.