高次非球面光路计算中的两个重要问题

提出在高次非球面的光路计算中运用变曲率的“辅助球面”概念,对某些文献在此方面存在的问题进行分析,提出迭代逼近精度的数值判据及浮动处理方法。     

Low-energy points on the sphere and the real projective plane

We present a generalization of a family of points on ${\mathbb{S}}^2$, the Diamond ensemble, containing collections of N points on ${\mathbb{S}}^2$ with very small logarithmic energy for all $N\in \mathbb{N}$. We extend this construction to the real projective plane ${\mathbb{RP}}^2$ and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.     

Deflagration-to-detonation transition process for spherical aluminum dust/epoxypropane mist/air mixtures in a large-scale experimental tube

The deflagration-to-detonation transitions (DDTs) for clouds of spherical aluminum dust (SAD) mixed with air or epoxypropane mist (EPM) and air were investigated in a 29.6-m-long experimental tube of 199 mm in diameter. The clouds formed through the injection of SAD and SAD/liquid epoxypropane samples into the experimental tube. Explosions of the SAD/air mixture were initiated using a 7-m-long EPM/air cloud explosion ignited by a 40-J electric spark. Explosions in SAD/EPM/air clouds were initiated using a 1...     

Characteristic behaviour of plasma fluctuations inside a plasma bubble in presence of a magnetic field due to the formation of a potential well

Experiments were carried out to observe the effect of a magnetic field and grid biasing voltage in presence of a plasma bubble in a magnetized, filamentary discharge plasma system. A spherical mesh grid of 80% optical transparency was negatively biased and introduced into the plasma for creating a plasma bubble. Diagnostics via an electrical Langmuir probe and a hot emissive probe were extensively used for scanning the plasma bubble. Plasma floating potential fluctuations were measured at three different positions of the plasma bubble. The instability in the pattern showed the dynamic transition from periodic to chaotic for increasing magnetic fields. Time scale analysis using continuous wavelet transform was carried out to identify the presence of non‐linearity from the contour plots. The mechanisms of the low‐frequency instabilities along with the transition to chaos could be qualitatively explained. Non‐linear techniques such as fast Fourier transform, phase space plot, and recurrence plot were used to explore the dynamics of the system appearing during plasma fluctuations. In order to demonstrate the observed chaotic phenomena in this study, characteristics of chaos such as the Lyapunov exponent were obtained from experimental time series data. The experimentally observed potential structure is confirmed with numerical analysis based on fluid hydrodynamics.     

Synthesis of glycerol-thiophene nanoparticles,a suitable sensing platform for voltammetric determination of guaifenesin

Boronic acid functionalized materials have gained much attention in both chemistry and biology fields due to their multivalent covalent interactions with cis-diol containing (macro) molecules. The remarkable progress in this field has resulted in the development of their biomedical applications, such as, biosensors and nanocarriers. In this study, the spherical nanoparticles consisting of glycerol and 2,5-thiophenediylbisboronic acid were synthesized by one-pot ring opening copolymerization of a mixture of glycidol and 2,5-thiophenediylbisboronic acid. The synthesized nanoparticles were used for the modification of the glassy carbon electrode and the determination of Guaifenesin. The synthesized polymeric nanoparticles were characterized by different spectroscopic and microscopic methods including UV–vis, IR, NMR, DLS, and SEM. Additionally, the electrochemical behavior of the fabricated electrode toward Guaifenesin was investigated with cyclic voltammetry and electrochemical impedance spectroscopy.     

Precipitated droplets in-situ cross-linking polymerization and its applications

A novel, green and effective approach to fabricate uniform functional spherical polymer particles remains a huge challenge. Herein, we present a novel one-pot approach superior to traditional precipitation polymerization, called precipitated droplets in-situ cross-linking (PDIC) polymerization, by which uniform particles are fabricated on large scale without any toxic organic solvents or stabilizers. With this approach, functional spherical polymer particles can be fabricated continuously only relying on gravity, and the preparation process is thus super-fast. For example, polyacrylic acid (PAA) hydrogel particles with ultra-high adsorption capacity are fabricated within only 60 s. Moreover, we have successfully fabricated different functional hydrogel particles, including anticoagulant, reinforced and bactericidal particles, based on the monomers of 2-acrylamide-2-methylpropanesulfonic acid (AMPS), acrylamide (AM) and [2-(methacryloyloxy)ethyl]trimethylammonium chloride (DMC), respectively. This approach has several advantages: (i) the technology is green; (ii) the size and porosity of the particles can be well-controlled; (iii) various functional spherical hydrogel particles can be fabricated by using corresponding monomers. More importantly, this approach fits the commercialization of functional hydrogel particles on demand.     

The zero curvature equation for rigid CR-manifolds

In this paper, we present the general analytic solution to the zero curvature equation for rigid three-dimensional CR-manifolds. The solutions are uniquely determined by one function and four real parameters.     

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.     

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。