Guo族约束流的经典Poisson结构、Lax表示、r-矩阵和Liouville可积性

基于伴随表示,通过引入Ｊａｃｏｂｉ－Ｏｓｔｒｏｇｒａｄｓｋｙ坐标,获得了Ｇｕｏ族约束流的Ｌａｘ表示,Ｐｏｉｓｓｏｎ结构和ｒ－矩阵,最后,借助Ｐｏｉｓｓｏｎ结构和ｒ－矩阵,说明了Ｇｕｏ族约束 是Ｌｉｏｕｖｉｌｌｅ可积的。     

Pseudo-division algorithm for matrix multivariable polynomial and its application

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｒｏｂｌｅｍｏｆｇｉｖｅｎｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎａｎｄｓｅｅｋｉｎｇｉｔｓｅｑｕｉｖａｌｅｎｔＨａｍｉｌｔｏｎｉａｎｉａｎｓｙｓｔｅｍｂｅｌｏｎｇｓｔｏｉｎｖｅｒｓｅｐｒｏｂｌｅｍｏｆａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓ,ａｎｄｔｈｅｌａｔｔｅｒｉｓｏｎｅｏｆｐｒｉｍｅｐｒｏｂｌｅｍｓｉｎｃｌａｓｓｉｃａｌｍｅｃｈａｎｉｃｓ.ＴｈｅｆａｍｏｕｓＰｏｉｎｃａｒｅ＿ＣａｒｔｏｎｐｒｏｂｌｅｍｉｓｔｏｇｅｔｔｈｅＨａｍｉｌｔｏｎｉａｎｉａｎｒｅｇｕｌａ…     

2+1-维变系数广义Kadomtsev-Petviashvili方程的相似约化

借助于MATHEMATICA软件,将直接约化法推广并应用到2+1-维变系数广义Kadomtsev-Petviashvili(VCGKP)方程,获得了VCGKP方程的若干相似约化,其中包括PainleveⅠ型、PainleveⅡ型和PainleveⅣ型的约化.     

Preparation of Fe3O4@SiO2@MnO2 microspheres as an adsorbent for Th(IV) removal from aqueous solution

Journal of Radioanalytical and Nuclear Chemistry - A magnetic nano-composites Fe3O4@SiO2@MnO2 were fabricated for efficient removal of Th(IV) from aqueous solutions, and characterized by SEM, TEM,...     

非线性学习方法与非线性科学

本文立足于中国传统文化提出非线性学习方法, 使数学物理中国化、简单化、个性化. 从八卦的角度统一看待非线性科学中的孤子、混沌、分形和机器学习, 以诗联网引领学科之间的对话, 实现学科之间的乾坤大挪移.     

Numerical solutions of partial differential equations by discrete homotopy analysis method

This paper introduces a discrete homotopy analysis method (DHAM) to obtain approximate solutions of linear or nonlinear partial differential equations (PDEs). The DHAM can take the many advantages of the continuous homotopy analysis method. The proposed DHAM also contains the auxiliary parameter ?, which provides a simple way to adjust and control the convergence region of solution series. The convergence of the DHAM is proved under some reasonable hypotheses, which provide the theoretical basis of the DHAM for solving nonlinear problems. Several examples, including a simple diffusion equation and two-dimensional Burgers’ equations, are given to investigate the features of the DHAM. The numerical results obtained by this method have been compared with the exact solutions. It is shown that they are in good agreement with each other.     

Evaluation of glass-forming ability for bulk metallic glasses based on characteristic temperatures

A new criterion ω₂, defined as T_g/(2T_x?T_g)?T_g/T_l (wherein T_g is the glass transition temperature, T_x the onset crystallization temperature, and T_l the liquidus temperature), has been proposed to assess the glass-forming ability (GFA) of bulk metallic glasses (BMGs) based on the classical crystallization theory and the crystallization resistance. The analysis indicates that the factors T_g/(2T_x?T_g) and T_g/T_l could reflect the crystallization resistance and liquid phase stability of metallic glasses, respectively. From the available experimental data in literatures, the new criterion ω₂ has a better correlation with the GFA of metallic glasses than all other existing criteria such as T_rg(=T_g/T_l), ΔT_x(=T_x?T_g), γ(=T_x/(T_g+T_l)), ΔT_rg(=(T_x ? T_g)/(T_l ? T_g)), α(=T_x/T_l), β(=T_x/T_g + T_g/T_l), δ(=T_x/(T_l ? T_g)), φ(=T_rg(ΔT_x/T_g)^0.143), γ_m(=(2T_x ? T_g)/T_l), β(=T_x × T_g/(T_l ? T_x)²) and ξ(=ΔT_x/T_x+T_g/T_l). It has also been demonstrated that this ω₂ parameter is a simple and efficient guideline for exploring new BMG formers.     

Study on the adsorption and aggregation of dilute gemini surfactant solutions

As a function of temperature in aqueous solutions, the adsorption and aggregation of N,N’-bis (tetradecyl dimethyl)-1,2-dibromide-ethanediyl ammonium salt (GS14-2-14) and N,N’-bis (hexadecyl dimethyl)-1,2-dibromide-ethanediyl ammonium salt (GS16-2-16), were researched with drop-volume technique and conductometry, respectively. The results of surface tension measurements, which were analyzed by originally developed thermodynamic equations, illustrate that GS14-2-14 has a better surface activity and arranges more tightly in the adsorbed film than GS16-2-16. The data of conductivity were used to find critical micelle concentration (cmc) and counterion binding degree of micelle (β). Thermodynamic parameters of micellization were also obtained from the temperature dependence of cmc values. From the study, it is discovered that the micellization process is spontaneous and exothermic in nature and it is mainly driven by entropy.     

Dendrimer-based biosensor for chemiluminescent detection of DNA hybridization

We report on a highly sensitive chemiluminescent (CL) biosensor for the sequenc-specific detection of DNA using a novel bio barcode DNA probe modified with gold nanoparticles that were covered with a dendrimer. The modified probe is composed of gold nanoparticles, a dendrimer, the CL reagent, and the DNA. The capture probe DNA was immobilized on magnetic beads covered with gold. It first hybridizes with the target DNA and then with one terminal end of the signal DNA on the barcoded DNA probe. CL was generated by adding H₂O₂ and Co(II) ions as the catalyst. The immobilization of dendrimer onto the gold nanoparticles can significantly enhance sensitivity and gives a detection limit of 6 fmol L^-1 of target DNA.

正交场间隙中电子束动力学行为的研究

 用一维粒子模拟的方法对正交场平板二极管间隙中电子束的动力学行为进行了研究, 模拟结果表明: 注入电流存在着一个临界值, 当注入电流超过这个临界值时, 电子束的行为将由层流态变化到扰动态。当考虑相对论效应时, 这种由层流态到扰动态的中间过程较为明显, 且电流临界值突然下降, 与外加电压和磁场的关系不再是一个简单的单调递增关系。