The bifurcation and peakons for the special C (3, 2, 2) equation

In this paper, we investigate a special C(3, 2, 2) equation $$\begin{array}{@{}rcl@{}} u_{t}+ku_{x}-u_{xxt}+3(u^{3})_{x}=u_{x}(u^{2})_{xx}+u(u^{2})_{xxx}. \end{array} $$ The bifurcation and some new exact representations of peakons, bell-shaped solitary wave solutions and periodic cusp wave solutions for the equation are obtained using the qualitative theory of dynamical systems. It is shown that the peakons are actually the limit of bell-shaped solitary waves and periodic cusp waves. Moreover, a new characteristic of non-smooth solutions, two peakons coexisting for the same wave speed, is found. Some previous results are extended.     

短链聚苯乙烯稀溶液粘度及渗透压行为

本文用动态膜渗透压及粘度法测定了短链聚苯乙烯的分子量Mn, 第二virial系数A2及特性粘数[η], 得到聚苯乙烯(2.5×10^3, 均方末端距以及扩张因子αs均与报道值一致。本工作表明, 分子量大约在400-1.5×10^4之间, 为聚苯乙烯从小分子到高分子的过渡区, 此时短链聚苯乙烯以蠕虫形链存在于溶液中。     

B值随机元阵列加权和的完全收敛性

在随机元阵列随机有界的条件下,得到了行间独立B值随机元阵列加权和的完全收敛性成立的充分条件,延伸了文献[9]的主要结果和文献[6]的部分结果.     

测量单模波导参数的新方法:导模和漏模的双偏振测量

本文提出测量单模波导参数的新方法.用棱镜耦合器测量两种偏振基导模和基漏模的模折射率,并由相应的四个模方程确定单模波导参数.其测量精度优于纯导模测量.用这种方法测量了单模玻璃波导参数,并对误差来源作了理论分析.     

On the absolute stability of multi-nonlinear control systems in the critical cases

In this paper, we study the absolute stability of stationarymulti-nonlinear control systems in critical cases via a Liapunovfunction V of Lur type. Some necessary conditions are givenfor the existence of a Liapunov function. For systems for whichthe stability can be studied by using Lur-type functions, wegive the normal form, construct the optimal V function for thesystem, and present some (algebraic) criteria for absolute stability.     

A study of the behaviour of ampicillin in aqueous solution and thermodynamic characterization of its aggregation

The aggregation of ampicillin in water has been examined by conductivity measurements over the temperature range 288.15–313.15 K and light scattering. These measurements indicate the formation of two critical concentrations over the range 0–0.35 mol kg^?1. Aggregation number and effective aggregate charge were calculated from the static light scattering data according to the Anacker and Westwell treatment. Thermodynamic parameters of aggregate formation were obtained from a form of the mass action model applicable to systems of low aggregation number. This method was applied at both critical concentrations. A valence of one was used for the monomers present in the first equilibrium. The second equilibrium was between aggregates of two different sizes, in this case, the valence of the aggregates being the effective charge calculated from the Anacker and Westwell treatment. Experimental results show that free energies of micellization for ampicillin are higher for the first critical concentration and in the same range, but lower than for other penicillins. The enthalpies of micellization become negative when the temperature is increased, but the variation is three times greater for the first critical concentration than for the second.     

Thermodynamics of micellization of C7 and C8 lecithins

The surface tensions of the lecithins diheptanoyl- and dioctanoylphosphatidylcholine in phosphate medium, pH 7.4, have been measured over the temperature range 288.15–313.15K. Critical micelle concentrations, thermodynamic micellization parameters, adsorption parameters, transfer data of micelles to the aqueous surface and surface area minima per molecule were obtained from these measurements. Critical micelle concentrations slightly decrease with temperature. The micellization processes became increasingly exothermic with increase in temperature. The variation of Gibbs energies of transfer indicates that the processes are most favourable at low temperatures. From a study of entropy-enthalpy compensation phenomenon a compensation temperature of 300^?1 K^?1 was found, and from the intercept an analysis of the hydrophobic-hydrophilic balance was carried out.     

一类直径为2的极大平面图的Mostar指数

图G的Mostar指数定义为Mo(G)=∑uv∈Ε(G)|nu-nv|,其中nu表示在G中到顶点u的距离比到顶点v的距离近的顶点个数,nv表示到顶点v的距离比到顶点u的距离近的顶点个数.若一个图G的任两点之间的距离至多为2,且不是完全图,则称G是一个直径为2的图.已知直径为2点数至少为4的极大平面图的最小度为3或4.本文研究了直径为2且最小度为4的极大平面图的Mostar指数.具体说,若G是一个点数为n,直径为2,最小度为4的极大平面图,则(1)当n≤12时,Mostar指数被完全确定;(2)当n≥13时,4/3n2-44/3n+94/3≤Mo(G)≤2n2-16n+24,且达到上,下界的极图同时被找到.     

三水硝酸镝与苯并-15-冠-5在丙酮中配合行为的研究

本文为进一步弄清Dy(NO3)3.3H2O与B15C5在丙酮中的配合行为, 作者用改进的半微量相平衡方法, 研究了Dy(NO3)3.3H2O-B15C5-CH3COCH3三元体系在18℃时的溶解度, 并进一步分离制备配合物, 研究了配合物的红外光谱, 热力学等性质.     

捕食者-食饵-互惠交错扩散模型解的整体存在性

本文应用Sobolev嵌入定理,能量估计和bootstrap技巧证明一类捕食者-食饵-互惠交错扩散模型在空间维数小于10时古典解的整体存在性.