The index problem for eigenvalues for coupled boundary conditions and Fulton’s conjecture

This paper deals with regular self-adjoint Sturm–Liouville problems with coupled boundary conditions. The spectrum of the problems can be either bounded from below, or unbounded from both below and above. We consider the following question: given an eigenvalue, how to determine its index or indices efficiently? Using results on the level surfaces of the nth eigenvalue and certain inequalities among eigenvalues, the determination is converted into that of the index of the same eigenvalue for an appropriate separated boundary condition and hence can be achieved in terms of the Prüfer angle. As an application of this complete solution of the index problem, we show that Fulton’s conjecture about such an index is true.     

The discontinuous profile method for simulating two‐phase flow in pipes using the single component approximation

Godunov‐type algorithms are very attractive for the numerical solution of discontinuous flows. The reconstruction of the profile inside the cells is crucial to scheme performance. The non‐linear generalization of the discontinuous profile method (DPM) presented here for the modelling of two‐phase flow in pipes uses a discontinuous reconstruction in order to capture shocks more efficiently than schemes using continuous functions. The reconstructed profile is used to define the Riemann problem at cell interfaces by averaging of the components of the variable in the base of eigenvectors over their domain of dependence. Intercell fluxes are computed by solving the Riemann problem with an approximate‐state solver. The adapted treatment of boundary conditions is essential to ensure the quality of the computational results and a specific procedure using virtual cells at both extremities of the computational domain is required. Internal boundary conditions can be treated in the same way as external ones. Application of the DPM to test cases is shown to improve the quality of computational results significantly. Copyright © 2001 John Wiley & Sons, Ltd.     

On a stochastic wave equation with unilateral boundary conditions

We prove the existence and uniqueness of solutions to the initial boundary value problem for a one-dimensional wave equation with unilateral boundary conditions and random noise. We also establish the existence of an invariant measure.

     

由三氯丙烷粗馏分制取三醋酸甘油酯

三醋酸甘油酯工业上历来是用甘油与醋酸酯化制得[1],三醋酸甘油酯用作纤维素树脂和乙烯基聚合物、共聚物的增塑剂。主要用于增塑醋酸纤维素作卷烟过滤嘴,可提供良好的弹性、透气性和合适的硬度。工业上由氯丙烯生产环氧氯丙烷过程中,生产相当量的三氯丙烷(以下简称ＴＣＰ),1,3二氯2丙醇等副产品[2]。以齐鲁石化公司氯碱厂3.2×104ｔ/ａ环氧氯丙烷装置为例,副产物ＴＣＰ达2000ｔ/ａ。它们在生产中成为一个馏分分离出来。这一馏分没有什么用处,用燃烧法处理时还生成ＨＣｌ等废气污染环境[3],我们考虑将它转化为三醋酸甘油酯,既可以变废为宝又…     

Population model with diffusion and supplementary forest resource in a two-patch habitat

A mathematical model is proposed to study the role of supplementary self-renewable resource on species population in a two-patch habitat. It is assumed that the density of forest resource biomass is governed by the logistic equation in both the regions but with the different intrinsic growth rate but the same carrying capacity in the entire habitat. It is further assumed that the densities of species population is also governed by the generalized logistic equations in both the regions but with different growth rates and carrying capacities. It is shown that the steady state solutions are positive, monotonic and continuous under both reservoir and no-flux boundary conditions. The linear and non-linear asymptotic stability conditions of non-uniform steady state are compared with the case of the model with and without diffusion in a homogeneous habitat.     

目标属性为肯定和否定的多目标决策问题解的有效性条件

本文建立了一类目标属性为肯定和否定的多目标决策模型，定义了相应的有效性。并在此基础上，讨论了有效性条件。     

Open boundary condition symposium benchmark solution: Stratified flow over a backward-facing step

This paper presents a detailed numerical solution to a simplified version of two-dimensional stratified flow over a backward-facing step with a Froude number of 16/9, a Reynolds number of 800 and a Prandtl number of 1—one of the Open Boundary Condition Symposium test problems. The steady state solution was derived by integrating the time-dependent Boussinesq equations forward in time using a semi-implicit finite-element-based model on a 38400-element mesh. In addition to presenting the results derived on this grid, the paper also presents the results of a Richardson extrapolation calculation for a set of ‘key’ parameters. It is hoped that this solution can be used as a baseline to compare the performance of the various techniques discussed at the Open Boundary Condition Symposium.     

嗜铅菌对水中重金属Pb~(2+)的吸附研究

研究了实验室提供的嗜铅菌对水中铅离子吸附的条件和机理.讨论了吸附时间、pH、铅离子的质量浓度和菌的质量浓度对吸附的影响.结果表明,在pH=7.0、铅离子初始质量浓度为25mg/L、离心湿菌的质量浓度为1.06g/L、吸附时间为60min时,铅离子的吸附率达96.88%;实验条件下超标25倍的含Pb~(2+)废水,可迭排放标准;Pb~(2+)的最大吸附量为150mg/g.数学模型Langmuir和Freundlich方程均能很好地描述嗜铅菌对Pb~(2+)的吸附过程.对Pb~(2+)吸附前后的红外光谱表征表明,嗜铅菌表面多糖、蛋白质的羟基峰和羰基峰均有不同程度的紫移,羟基峰、糖苷峰等峰宽略增,说明菌体吸附,主要是表面基团的作用所致.用原子力显微镜对吸附前后的嗜铅菌检测可见,吸附后菌体的弹性变小、粘性变大、部分茵体有一定的收缩,说明以表面吸附为主的吸附过程,对菌细胞的聚合度有影响,菌体内部对铅也有一定的生物积累.     

一类二阶非线性微分方程多点共振边值问题的可解性

讨论了一类二阶非线性微分方程多点共振边值问题,通过运用Mawhin连续定理,我们在一个较简单的条件下得到了问题的解的存在性结果.     

A nonlocal nonlinear diffusion equation in higher space dimensions

We study the initial-value problem for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation, in the whole RN, N?1, or in a bounded smooth domain with Neumann or Dirichlet boundary conditions. First, we prove the existence, uniqueness and the validity of a comparison principle for solutions of these problems. In RN we show that if initial data is bounded and compactly supported, then the solutions is compactly supported for all positive time t, this implies the existence of a free boundary. Concerning the Neumann problem, we prove that the asymptotic behavior of the solutions as t→∞, they converge to the mean value of the initial data. For the Dirichlet problem we prove that the asymptotic behavior of the solutions as t→∞, they converge to zero.