Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice

The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.     

Pd-PAN催化制备拉帕替尼中间体的研究

本文以N-(3-氯-4-((3-氟苯基)甲氧基)苯基)-6-碘喹唑啉-4-胺为起始原料,经自制聚苯胺负载钯催化剂(Pd-PAN)催化Suzuki偶联反应制备N-(3-氯-4-(3-氟苄氧基)苯基)-6-((5-甲酰基)呋喃-2-基)-4-喹唑啉胺。对Pd-PAN的结构和理化性能进行表征。通过正交实验确定最佳反应条件:80℃下,催化剂与底物质量比为1∶40,乙醇溶剂体系进行Suzuki偶联反应。Pd-PAN回收使用5次,产物的转化率保持在85%以上。以此中间体合成拉帕替尼,通过熔点测定、HPLC、质谱、~1H-NMR对终产物进行了结构确证。本工艺操作简单,产品质量稳定,适于工业扩大生产。     

新型内表面反相限进填料的制备与评价

通过在硅烷化硅胶内表面和外表面分别键合己胺和聚乙烯醇,制备了能够在线直接进样分析生物样品的新型内表面反相限进填料。采用元素分析、电镜观察对该限进填料的结构进行了表征。以普萘洛尔、阿替洛尔、苯巴比妥、卡马西平作溶质探针,并以Merck公司生产的限进填料柱作参比,对合成的限进填料的色谱性能进行了研究。研究结果表明,所制备的限进填料有较好的蛋白质排阻能力、富集能力和反相色谱性能,能同时实现排阻生物大分子杂质和富集小分子被分析物的功能,可作为在线、快速直接进样检测分析生物样品的预处理柱,适用于普萘洛尔血浆的直接进样分析。     

Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations

In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm （CH） and Degasperis Procesi （DP） shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformatioas back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems.     

离散修正KdV方程的解析近似解

将同伦分析法进行了推广,使之适用于求解离散修正KdV方程.获得了由指数函数表达的亮孤子解,该解析近似解与精确解符合很好.数值模拟结果说明了同伦分析法对求解复杂非线性问题的有效性和潜力.