Symmetry Analysis and Conservation Laws to the(2+1)-Dimensional Coupled Nonlinear Extension of the Reaction-Diffusion Equation

In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem.     

Novel exact solutions of coupled nonlinear Schro¨dinger equations with time–space modulation

We construct various novel exact solutions of two coupled dynamical nonlinear Schrdinger equations.Based on the similarity transformation,we reduce the coupled nonlinear Schrdinger equations with time-and space-dependent potentials,nonlinearities,and gain or loss to the coupled dynamical nonlinear Schrdinger equations.Some special types of non-travelling wave solutions,such as periodic,resonant,and quasiperiodically oscillating solitons,are used to exhibit the wave propagations by choosing some arbitrary functions.Our results show that the number of the localized wave of one component is always twice that of the other one.In addition,the stability analysis of the solutions is discussed numerically.     

利用17O固体核磁共振波谱分析Ni/CeO2表面镍离子含量

本文以具有重要催化应用前景的Ni/CeO₂体系为例，借助¹⁷O固体核磁共振波谱技术，根据表面氧物种¹⁷O NMR信号的变化，尝试分析了Ni/CeO₂表面层中镍离子的含量.分析结果显示，10% NiCe-500和20% NiCe-300两种Ni/CeO2样品表面第一和第二金属离子层中Ni离子的含量分别位于9%~17%和8%~15%范围内.这一方法或可推广至研究其它一系列顺磁掺杂氧化物的表面掺杂含量.     

Solutions to Nonlocal Integrable Discrete Nonlinear Schr?dinger Equations via Reduction

Solutions to local and nonlocal integrable discrete nonlinear Schr?dinger(IDNLS) equations are studied via reduction on the bilinear form. It is shown that these solutions to IDNLS equations can be expressed in terms of the single Casorati determinant under different constraint conditions.     

石墨烯修饰改性制备锂离子电池LiFePO4/LiNi0.8Co0.15Al0.05O2复合正极材料及其性能

采用两步干混-球磨方法制备了石墨烯掺杂改性的锂离子电池LiFePO_4/LiNi_(0.8)Co_(0.15)Al_(0.05)O_2复合正极材料,实现LiNi_(0.8)Co_(0.15)Al_(0.05)O_2材料的高容量和高安全性。借助X射线衍射(XRD)、扫描电镜(SEM)、透射电镜(TEM)、X射线光电子能谱(XPS)以及电化学测试等表征手段对材料的晶体结构、微观形貌和电化学性能进行了较系统的研究。结果表明,石墨烯的存在实现了Li Fe PO4材料在LiNi_(0.8)Co_(0.15)Al_(0.05)O_2材料表面的完全包覆,形成致密的包覆层,进一步抑制LiNi_(0.8)Co_(0.15)Al_(0.05)O_2与电解液之间的副反应,提高活性材料利用率和循环性能。三者之间构成导电网络,加快电子渗透和传输,提高倍率性能。Li Fe PO4质量分数为20%的Li Fe PO4-Graphene/LiNi_(0.8)Co_(0.15)Al_(0.05)O_2样品具有最佳的容量性能和长循环性能,0.1C时放电容量达到202.5 m Ah·g~(-1),3C时放电容量仍然可保持在160.5 m Ah·g~(-1)。50℃在2.8~4.3 V,0.5C下循环100次后,容量保持率为91.9%,优于LiNi_(0.8)Co_(0.15)Al_(0.05)O_2和LiFePO_4/LiNi_(0.8)Co_(0.15)Al_(0.05)O_2样品的72.9%和82.0%。     

Nonlocal Symmetry and Explicit Solution of the Alice-Bob Modified Korteweg-de Vries Equation

Nonlocal symmetry and explicit solution of the integrable Alice-Bob modified Korteweg-de Vries(ABm Kd V) equation is discussed, which has been established by the aid of the shifted parity and delayed time reversal to describe two-place events. Based on the Lax pair which contains the two-order partial derivative, the Lie symmetry group method is successfully applied to find the exact invariant solution for the AB-m Kd V equation with nonlocal symmetry by introducing one suitable auxiliary variable. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to some specific functions are derived. Figures show the physical phenomenon, that is, "the shifted parity and delayed time reversal to describe two-place events".     

氧化物纳米材料表面结构与性质的固体核磁共振波谱研究

氧化物纳米材料的多种应用与其表面结构和性质密切相关.近年来,固体核磁共振波谱在相关研究中提供了关键信息.本综述总结了近期发展的、以固体核磁共振波谱为主的两种表征氧化物纳米材料表面结构和性质的方法,包括表面选择的同位素标记¹⁷O核磁共振波谱与动态核极化表面增强核磁共振波谱,并对氧化物纳米材料的固体核磁共振波谱研究的发展趋势进行了展望.     

Pfaffian-Type Soliton Solution to a Multi-Component Coupled Ito Equation

Multi-soliton solution to a multi-component coupled Ito system is investigated based on the Hirota bilinear method. By virtue of the perturbation method, we firstly derive one- and two-soliton solutions for the coupled Ito system possessing four components. Then the multi-soliton solution for the multi-component coupled Ito system is summarized into a general form expressed by pfaffians. Finally, this general pfaffian-type soliton solution is proved by pfaffian techniques.     

Darboux Transformations via Lie Point Symmetries： KdV Equation

By localizing the nonlocal symmetries of a nonlinear model to local symmetries of an enlarged system, we find Darboux-Backlund transformations for both the original and prolonged systems. The idea is explicitly realized for the well-known KdV equation.     

Novel exact solutions of coupled nonlinear Schrōdinger equations with time-space modulation

We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrrdinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.