完整Coriolis力作用下带有外源强迫的非线性KdV方程

利用摄动方法,从描写既有Coriolis力垂直分量又含有水平分量的位涡方程出发,给出了近赤道非线性Rossby波所满足的具有外源强迫的非线性KdV方程,并利用Jacobi椭圆函数展开法,求解了改进后的非线性KdV方程的行波解及孤立波解.通过分析KdV方程的行波解,指出Coriolis力的水平分量和外源对Rossby波动的影响.     

完整Coriolis力作用下的非线性Rossby波

在正压流体中,利用摄动方法从描写既有Coriolis参数的垂直分量又含有水平分量的位涡方程出发,推导了近赤道非线性Rossby波振幅演变所满足的非线性mKdV方程,并利用Jacobi椭圆函数展开法,求解了推广后的非线性mKdV方程的行波解及孤立波解.通过分析其方程的行波解及孤立波,表明地球旋转的水平分量对Rossby波动产生一定的影响.     

新型壳聚糖固相微萃取薄膜的研制及性能研究

壳聚糖是一种富含氨基和羟基的天然高分子聚合物,易成膜,膜的机械性能、透光率好,且膜的表面平整光滑,对叶绿素有较高的富集能力,平衡态时叶绿素在壳聚糖膜和水相两相间的分配系数为9090,重现性好,可以研制成固相微萃取薄膜用于叶绿素的分析。磁力搅拌萃取叶绿素,壳聚糖膜可在80 min内达到平衡,用5％NaOH超声洗脱30 min内可以洗脱干净。红外光谱和X射线衍射谱图表明萃取叶绿素之后的壳聚糖分子中分子内或分子间的氢键作用力大大减弱,可能是壳聚糖分子中的大量氨基和羟基在萃取叶绿素的过程中起关键作用。     

A kind of extended Korteweg——de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio $\varepsilon $, represented by the ratio of amplitude to depth, and the dispersion ratio $\mu $, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin {\it et al} in the study of the surface waves when considering the order up to $O(\mu ^2)$. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin {\it et al} for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.     

Dynamics analysis in a tumor-immune system with chemotherapy

An ordinary differential equation (ODE) model of tumor growth with the effect of tumor-immune interaction and chemotherapeutic drug is presented and studied. By analyzing the existence and stability of equilibrium points, the dynamic behavior of the system is discussed elaborately. The chaotic dynamics can be obtained in our model by equilibria analysis, which show the existence of chaos by calculating the Lyapunov exponents and the Lyapunov dimension of the system. Moreover, the action of the infusion rate of the chemotherapeutic drug on the resulting dynamics is investigated, which suggests that the application of chemotherapeutic drug can effectively control tumor growth. However, in the case of high-dose chemotherapeutic drug, chemotherapy-induced effector immune cells damage seriously, which may cause treatment failure.     

舟山岛潮间带沉积物和生物中砷质量分数测定及评价

应用氢化物发生-原子荧光光谱方法（HC-AFS）研究了舟山岛海域沉积物和生物样中砷的质量分数并进行了评价．结果如下：1．建立方法的线性方程为：If（As）=6．1669C-1．0649,方法的检出限为0．2ng／mL,该法测定两种标准样品的偏差分别为-6．6％和0．2％．2．沉积物和生物体中均检测到一定量的砷,沉积物中砷质量分数为：12．33～16．49μg／g,生物样中质量分数为：1．31～17．25μg／g．参考海洋沉积物和生物质量标准,前者属于一类沉积物,后者属于二类海洋生物;参考FAO／WHO建议的每日摄入总量,适当食用此类海洋生物是安全的．     

化疗对癌细胞数学模型稳态解的影响

本文基于Lotka-Volterra竞争方程提出了一个包含癌细胞与健康宿主细胞两种细胞群在内的动力学模型,研究了持续化疗对系统稳态解的影响.讨论了该系统达到稳态时,解的三种可能情况:癌细胞与健康细胞共存,癌细胞被根除以及健康细胞被灭活.通过对系统解的进一步理论分析,得到了解的存在性和全局渐近稳定性的充分条件.数值模拟进一步验证了理论结果.同时还发现,系统的稳态解与化疗药物的输注速率和化疗药物对癌细胞的杀伤率有关.研究表明在我们的模型中高浓度的化疗药物有可能完全根除癌细胞,但阈值取决于药物对癌细胞的杀伤系数(不考虑细胞突变及耐药性的产生).而对于癌症治疗而言,加强对癌细胞的杀伤率比提高药物剂量更效.