Darboux Transformation for Tzitzeica Equation

We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem. The explicit solution of Tzitzeica equation is obtained.     

Extended Riccati Equation Rational Expansion Method and Its Application to Nonlinear Stochastic Evolution Equations

In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.     

Variable Separation and Exact Separable Solutions for Equations of Type uxt=A(u,ux)uxx+B(u,ux)

The generalized conditional symmetry is developed to study the variable separation for equations of type u_xt=A(u,u_x)u_xx+B(u,u_x). Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their exact separable solutions are constructed.     

Scale-Free Properties in Traffic System

In this work, we propose a new model of evolution networks, which is based on the evolution of the traffic flow. In our method, the network growth does not take into account preferential attachment, and the attachment of new node is independent of the degree of nodes. Our aim is that employing the theory of evolution network, we give a further understanding about the dynamical evolution of the traffic flow. We investigate the probability distributions and scaling properties of the proposed model. The simulation results indicate that in the proposed model, the distribution of the output connections can be well described by scale-free distribution. Moreover, the distribution of the connections is largely related to the traffic flow states, such as the exponential distribution (i.e., the scale-free distribution) and random distribution etc.     

LBO晶体超光滑表面抛光机理

胶体SiO2抛光LBO晶体获得无损伤的超光滑表面,结合前人对抛光机理的认识,探讨了超光滑表面抛光的材料去除机理,分析了化学机械抛光中的原子级材料去除机理.在此基础上,对胶体SiO2抛光LBO晶体表面材料去除机理和超光滑表面的形成进行了详细的描述,研究抛光液的pH值与材料去除率和表面粗糙度的关系.LBO晶体超光滑表面抛光的材料去除机理是抛光液与晶体表面的活泼原子层发生化学反应形成过渡的软质层,软质层在磨料和抛光盘的作用下很容易被无损伤的去除.酸性条件下,随抛光液pH值的减小抛光材料的去除率增大;抛光液pH值为4时,获得最好的表面粗糙度.     

硫缺陷型In2S3光催化剂高效分解水制氢研究

缺陷工程被认为是提高光催化剂分解水制氢性能的关键策略之一,然而有关缺陷诱导半导体材料电子结构演变并增强光生载流子传输机制尚不明确。在本研究中,我们通过简单的一步水热合成法成功构建了富含S缺陷的In2S3半导体光催化剂（VS-In2S3）,在模拟太阳光辐照下其光催化分解水产氢性能相比传统的In2S3（P-In2S3）提升了近一个数量级（达到221.18 μmol/g/h）。此外,利用自主研发的原位X射线光电子能谱（SI-XPS）结合相关密度泛函理论计算证实：S缺陷可诱导强还原性的低价态In（In(3-x)+）暴露,进而增强In位点对H2O的吸附和活化能力,因此,S缺陷型In2S3表现出显著增强的光催化析氢活性。此外,可视化观测到H2O分子在原位光照下脱质子转化为OH的分解水制氢过程。该研究为缺陷型光催化剂设计及光催化分解水反应机制和过程研究提供了一定的见解。     

A New Supramolecular Tetraruthenated Cobalt (II) Porphyrazine Displaying Outstanding Electrocatalytical Performance in Oxygen Evolution Reaction

A new supramolecular electrocatalyst for Oxygen Evolution Reaction (OER) was synthesized from a central multibridging cobalt tetrapyridylporphyrazine (CoTPyPz) species by attaching four [Ru(bpy)₂Cl]⁺ groups. Both CoTPyPz and the tetraruthenated cobalt porphyrazine species, TRuCoTPyPz, form very homogenous molecular films just by dropcasting their methanol solutions onto GCE electrodes. Such films exhibited low overpotentials for O₂ evolution, e.g., 560 e 340 mV, respectively, displaying high stability, typically exceeding 15 h. The kinetic parameters obtained from the Tafel plots showed that the peripheral complexes are very important for the electrocatalytic activity. Hyperspectral Raman images taken along the electrochemical process demonstrated that the cobalt center is the primary active catalyst site, but its performance is enhanced by the ruthenium complexes, which act as electron-donating groups, in the supramolecular system.     

一类发展方程柯西问题的变换迭代法

潘涛在[2]中提出了高维波动方程柯西问题的变换迭代法,本文对其进行了推广.在初始数据和自由项为多元多项式的情况下,得到了包括双曲型、抛物型方程柯西问题在内的一类发展方程的求解格式,用其可迅速得到解的表达式.如果定解问题是适定的,由于多元多项式可以逼近连续函数,故方程的近似解可以转化为逼近问题,这在计算上是很有意义的.此外,笔者还提出了“模型初始数据法”的概念.     

出境旅游网络关注度时空演变及影响因素研究——以泰国为例

网络关注度是测量潜在旅游者对目的地旅游关注情况及需求变化的重要手段之一。基于百度指数,以我国31个省（区、市）（不含港、澳、台）的泰国旅游网络关注度为研究对象,运用季节性强度指数、地理集中度指数、赫芬达尔-赫希曼指数、地理探测器等方法,探讨我国居民对泰国旅游网络关注度的时空演化规律及其影响因素。结果表明：从时序演化上看,2011—2019年泰国旅游网络关注度呈波动上升态势,可划分为快速上升期和平稳发展期2个阶段,地区季节性差异显著,3月、7月、12月为泰国旅游网络关注度的高峰时段;从空间分异上看,泰国旅游网络关注度空间分异变化不大,空间集聚趋于分散状态,整体呈“东高-西低”的阶梯状递减特征,高关注度地区主要集中在东部地区及四川省,低关注度地区则主要分布于除四川省外的西部省份;从影响因素上看,经济发展水平（人均可支配收入、GDP）、交通便利程度、贸易开放度以及国际旅游开放度共同影响泰国旅游网络关注度的空间分布格局。     

Efficient and Stable Bifunctional Electrocatalysts Ni/NixMy (M = P,S) for Overall Water Splitting

Development of easy‐to‐make, highly active, and stable bifunctional electrocatalysts for water splitting is important for future renewable energy systems. Three‐dimension (3D) porous Ni/Ni₈P₃ and Ni/Ni₉S₈ electrodes are prepared by sequential treatment of commercial Ni‐foam with acid activation, followed by phosphorization or sulfurization. The resultant materials can act as self‐supported bifunctional electrocatalytic electrodes for direct water splitting with excellent activity toward oxygen evolution reaction and hydrogen evolution reaction in alkaline media. Stable performance can be maintained for at least 24 h, illustrating their versatile and practical nature for clean energy generation. Furthermore, an advanced water electrolyzer through exploiting Ni/Ni₈P₃ as both anode and cathode is fabricated, which requires a cell voltage of 1.61 V to deliver a 10 mA cm^?2 water splitting current density in 1.0 m KOH solution. This performance is significantly better than that of the noble metal benchmark—integrated Ni/IrO₂ and Ni/Pt–C electrodes. Therefore, these bifunctional electrodes have significant potential for realistic large‐scale production of hydrogen as a replacement clean fuel to polluting and limited fossil‐fuels.