Interaction of methyltin(IV) compounds with carboxylate ligands. Part 2: formation thermodynamic parameters,predictive relationships and sequestering ability

Thermodynamic data of mono‐, di‐ and tri‐methyltin(IV)‐carboxylate complexes (acetate, malonate, succinate, oxydiacetate, diethylenetrioxydiacetate, malate, citrate, 1,2,3‐tricarballylate, 1,2,3,4‐butanetetracarboxylate, 1,2,3,4,5,6‐benzenehexacarboxylate) in aqueous solution are reported at t = 25 °C and I = 0 mol l⁻¹. Thermodynamic parameters obtained were analysed to formulate empirical predictive relationships as a function of different parameters, such as the number of carboxylate groups of the ligand and the charge of the alkyltin(IV) cation. Sequestration diagrams of citrate and 1,2,3‐tricarballylate towards alkyltin(IV) cations at different pH values are also reported and discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Epidemic dynamics in a heterogeneous incompletely isolated population with allowance for seasonal variations in the infection rate

Mathematical parasite-host models are generalized to the case when the population members differ in susceptibility and contagiousness, there is an external source of infection, and the model parameters depend periodically (seasonally) on time. The model is proved to have a periodic solution that is unique and exponentially stable for sufficiently small periodic oscillations of the coefficients.     

Propagation of perturbations in a two-layer stratified fluid with an interface excited by moving sources

Propagation of small perturbations in a two-layer inviscid stratified fluid is studied. It is assumed that the higher density fluid occupies the lower unbounded half-space, while the lower density fluid occupies the upper unbounded half-space. The source of the excitation is a plane wave traveling along the interface of the fluids. An explicit analytical solution to the problem is constructed, and its existence and uniqueness are proved. The long-time wave pattern developing in the fluids is analyzed.     

一类具偏差变元的二阶微分方程周期解

By using the theory of coincidence degree,we study a kind of periodic solutions to second order differential equation with a deviating argument such as x"(t) f(x'(t)) h(x(t))x'(t) g(x(t-τ(t)))=p(t),some sufficient conditions on the existence of periodic solutions are obtained.     

向量优化问题有效解的稳定性

运用标量化的方法,通过锥正定真有效解的上半连续性讨论了无限维赋范空间中锥有效解的部分上半连续性,证明了锥有效解的通有稳定性.在此基础上,进一步证明,在Baire纲的意义下,绝大多数的向量优化问题至少存在一个锥正定真有效解是本质的有效解,换句话说,绝大多数的向量优化问题锥有效解是几乎下半连续的.     

一端固支一端简支变厚度梁的弹性力学解

研究了一端固支另一端简支连续变厚度梁在静力荷载作用下的应力和位移分布.通过引入单位脉冲函数和Dirae函数,将固支边等效为简支边与未知水平反力的叠加,利用平面应力问题的基本方程,导出满足控制微分方程及左右两端边界条件的位移函数的一般解,对上下表面的边界方程作Fourier级数展开,结合固支边位移为O的条件确定待定系数,得到的解是高精度的.数值结果与商业有限元软件ANSYS进行了比较,显示出很好的精度.     

广义变系数Kdv方程的对称及其群不变解

利用经典李对称的方法对广义变系数Kdv方程进行研究,利用这种方法得到了该方程的一个新的精确解,这种方法的基本思路是通过对称约化将原来较难求解的偏微分方程转化为较易求解的常微分方程进行求解.实例证明这种方法具有一般性,适合于求一大类变系数的非线性演化方程.     

带捕食者密度制约的Lotka-Volterra模型概周期解的存在性

利用指数型二分性及不动点方法讨论了一类带捕食者密度制约的Lotka-Volterra模型,得出了模型的概周期解的存在性定理.     

多阶段M-SV投资组合优化的离散近似迭代法研究

文章提出了离散近似迭代法,用该方法求解具有交易成本和交易量限制的多阶段均值一半方差(M-sV)投资组合模型.离散近似迭代方法的基本思路为:首先,将连续型状态变量离散化,根据网络图的构造方法将上述模型转化多阶段赋权有向图;其次,运用嘉量原理求出起点至终点的最长路程,即获得模型的一个可行解;最后,以该可行解为基础,继续迭代直到前后两个可行解非常接近.文章还证明了该方法的收敛性和复杂性.     

带捕食者密度制约的Lotka—Volterra模型概周期解的存在性

利用指数型二分性及不动点方法讨论了一类带捕食者密度制约的Lotka—Volterra模型，得出了模型的概周期解的存在性定理．