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.     

Broer-Kaup系统的达布变换和新的精确解

利用Broer-Kaup系统Lax对的两个基本解，构造了该系统一个新的达布变换，并利用该变换求出了Broer-Kaup系统一组新的双向孤子解. 关键词： Lax对 达布变换 孤子解     

系统动力学方法在规划研究中的应用——大连市种植业系统动力学模型的研究

本文运用系统动力学方法,对大连种植业系统进行了定性分析,建立了定量模型——系统动力学模型,对该市的种植业生产进行了动态建模、仿真和预测。为大连市种植业发展“八五”计划及十年规划的制定提供了科学依据。     

5-[{4-[2-(5,6,7,8-四氢-5,5,8,8-四甲基)萘氧-2-基]乙氧基}苄基]-2,4-噻唑烷二酮的合成

以2,5-二甲基-2,5-己二醇为原料,经氯化、傅一克反应、烷化、Knoevenagel缩合、还原反应制得5-【{4-[2-(5,6,7,8-四氢-5,5,8,8-四甲基)萘氧-2-基]乙氧基}苄基】-2,4．噻唑烷二酮,其结构经元素分析,IR和1H NMR证实。总收率6．3％。     

共固定化TNF-α/IFN-γ对宫颈癌HeLa细胞的长效抑制作用

利用光化学固定方法,将TNF-α/IFN-γ共同固定在组织培养聚苯乙烯培养孔内,选择最佳固定细胞因子剂量20ng/well,对HeLa细胞行长效性实验研究.培养时间为1d、2d、3d、4d、5d和6d.同时设游离TNF-α+IFN-γ与纯无血清培养对照组.计算TNF-α/IFN-γ共固定药物对HeLa细胞抑制率.并采用荧光显微镜及流式细胞仪行Hoechst 33258染色定性分析和磷脂酰丝氨酸外翻定量分析细胞凋亡.结果表明低剂量20ng/well的共固定细胞因子对HeLa细胞的生长抑制具有时间效应,作用第5d抑制率达到92%,游离细胞因子作用第3d达到最大抑制率76%,第6d抑制率减少到41%.Hoechst 33258细胞形态学研究显示,药物作用6d时,20ng/well共固定细胞因子诱导的凋亡效果比游离细胞因子的更为显著.流式细胞仪磷脂酰丝氨酸外翻定量分析表明作用第6d,20ng/well共固定药物诱导宫颈癌细胞早中期凋亡的比率比同样浓度游离药物凋亡率高14.8%.经光化学固定后低剂量细胞因子TNF-α/IFN-γ具有抑制HeLa细胞生长与诱导HeLa细胞凋亡的活性,并且共固定化细胞因子的抑癌活性和药效持续性比游离细胞因子显著.     

一类具不变性质的变系数偏微分方程的特解

In this paper, a few properties of general patial differential operator P beinginvariant with respect to the form F(|x|_p^p+|y|_q^q-|z|_r^r) are studied, where x∈Rⁿ,y∈ R^m, z∈R^l.and explicit formulas are given for certain solution of the equation Pu=Aδ with P being a differential operator with power function coefficientswhich preserves the form (|x|_p^p+|y|_q^q-|z|_r^r)^1/v for arbitrary even integers p, q, r,and odd integers v.     

线性齐次偏微分方程组的既约化基

本文参照代数Grobner基的思想,提出线性齐次偏微分方程组的既约化基的概念, 并给出了线性齐次偏微分方程组的既约化基的唯一性定理.