Lame equation and asymptotic higher-order periodic solutions to nonlinear evolution equations

Based on an auxiliary Lame equation and the perturbation method, a direct method is proposed to construct asymptotic higher-order periodic solutions to some nonlinear evolution equations. It is shown that some asymptotic higher-order periodic solutions to some nonlinear evolution equations in terms of Jacobi elliptic functions are explicitly obtained with the aid of symbolic computation.     

On the interaction between dislocations and cracks in one-dimensional hexagonal quasi-crystals

The solution of elasticity problems involving the interaction between dislocations and cracks plays a fundamental role in many practical and theoretical applications. Although elasticity problems involving dislocation or cracks in quasi-crystals have been investigated in many papers, the analysis is limited to a single defect. This paper investigates the interaction of defects in one-dimensional hexagonal quasi-crystals using the complex variable function method. The interaction force between two parallel dislocations is presented and the analytic solutions of elastic fields of interaction between a dislocation and a crack are obtained. A version of the well-known Peach－Koehler formula in one-dimensional hexagonal quasi-crystals is given.     

New Exact Solutions of Broer-Kaup Equations

Based on a known transform, the exact solutions of (2 1)-dimensional Broer-Kaup equations are investigated by using the method of direct integral. A kind of new exact solutions of Broer Kaup equations are obtained,which contain previous results about solitary wave solutions.     

Icosahedral quasicrystals solids with an elliptic hole under uniform heat flow

The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors is presented.     

Periodic solutions of nonlinear Schro^edinger type equations

By using the solutions of an auxiliary elliptic equation, a direct algebraic method is proposed to construct the exact solutions of nonlinear Schrfdinger type equations. It is shown that many exact periodic solutions of some nonlinear Schro^edinger type equations are explicitly obtained with the aid of symbolic computation, including corresponding envelope solitary and shock wave solutions.     

一般变换下的Jacobi椭圆函数展开法及应用

将在行波变换下的Jacobi椭圆函数展开法推广到范围非常广泛的一般函数变换下进行，利用这一方法求得了一些非线性发展方程的精确周期解，这些解包括了在行波变换下所求得的周期解. 证明了一些非线性发展方程的周期解一定是行波解. 关键词： 非线性发展方程 周期解 行波解 Jacobi椭圆函数     

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.     

一维六方准晶中螺形位错与楔形裂纹的相互作用

采用保角映射方法和扰动技巧,研究了一维六方准晶中螺形位错和半无限楔形裂纹的相互作用. 讨论了位错的位置和楔形角对作用在位错上的力的影响,得到了应力强度因子和作用在 位错上的力的解析解.此外,还详细地讨论了位错对裂纹的影响.当楔形角参数λ=1/2时, 半无限楔形裂纹退化成半无限尖裂纹,相应的结果 可以作为特殊情况而直接得到.     

超声法制备Au/Fe3O4及其催化还原4-硝基苯酚性能

通过简易的超声法以及原位还原法成功制备出了负载型可再生Au/Fe₃O₄催化剂。利用3-氨丙基三乙氧基硅烷（APTES）作为有机桥键,将Au固定在Fe₃O₄的表面,得到单分散磁性Au/Fe₃O₄。Au⁰在氨基的作用下不会团聚,因此具有较高的催化活性及稳定性。XRD、HRTEM、EDS和XPS等测试结果表明Au/Fe₃O₄已被成功制备。将其用于催化还原4-硝基苯酚得到4-氨基苯酚,表现出较高的催化活性,速率常数可达0.225 6 min^-1。重复性实验表明该催化剂具有良好的稳定性,反应9个循环之后,催化还原反应的转化率仍可达到94%。     

One-pot co-precipitation of copper–manganese–zinc oxide catalysts for the oxidation of CO and SO2 in the presence of ultrasonic irradiation

Research on Chemical Intermediates - This paper studies the effect of addition of Zn and ultrasound-assisted co-precipitation on Cu-Mn oxide catalysts for the oxidation of CO. Cu-Mn-Zn oxide...