潜水污染问题数学模型的广义解

讨论了具有混合边界的潜水污染数学模型，在适当条件下，应用Galerkjn方法证明了模型广义解的存在性，并证明了广义解的唯一性和对初边值及自由项的连续依赖性．     

格群的扭自由根式

格群的扭自由根式仝道荣（河海大学，南京２１００２４）我们利用［１，２］中的术语及符号。设Ｔ及Ｔ′分别为所有扭类自和所有扭自由类的集￣［３．４］．一个扭自由称作是遗传的，如果对任意的ｌ－，群Ｇ，蕴含着Ｇ／ＨＥ令Ｔ′为所有拟遗传扭自由类的集。定理１假定那...     

任意边界条件下圆柱厚壳自由振动分析的空间变量变换法

本文提出一种一般解析方法——空间变量变换法,用以求解任意边界条件下圆柱厚壳自由振动问题.运用本文方法对悬臂圆柱厚壳的自振特性作了计算,计算结果与薄壳理论相应结果及试验值作了比较.理论分析和计算结果表明,本文方法具有很好的收敛性和精确性,可以推广用于分析梁、板、壳的自由振动.     

关于横泾浜上的工业排污最经济方案的研究

摘要(略) 　　一、前言(略) 　　二、正文 　　(一)问题的来源 　　对河流的污染主要来自于生活废水和工业废水,其中工业废水尤为严重.我国每年的废水排放总量达420亿吨左右,其中工业废水排放总量达229亿吨左右,占总量的54.5%,且工业废水对水质的污染更为严重,有必要对其实施更严格的水质污染总量控制.……     

对一个治污问题的探究

问题　有一个湖泊 ,上游有一水流以每天15 0 0ｍ3的水流入该湖 ,水流内含某种不能自然分解的污染物质 ,在湖的出口每天流出湖泊的水也为15 0 0ｍ3,湖水体积保持在 2 0 0万ｍ3左右 .现假设下雨和蒸发正好平衡 ,且该污染物质与湖水能很均匀地混合 ,并测得湖水中该污染物质量分数已达到 0 .2 ｇ/ｍ3.由于政府治污 ,目前上游污染已得到治理 ,流入湖中的水已不再含该污染物 .1)试求上游污染物中止后第ｎ天 ,湖水的该污染物质量分数 ;2 )欲使湖水水质达到该污染物质量分数不超过 0 .0 5 ｇ/ｍ3的标准 ,若不采取其它治污措施 ,湖水需要多少天才可以…     

CPM网络中机动时间的使用效率及应用

本文研究CPM网络计划中总时差和单时差的使用效率问题及在项目管理中的应用.文章首先探讨了总时差和自由时差的使用对CPM网络中新关键路线形成的影响,得出结论:一般情况下一条路线上各工序分别使用自由时差的方式比某个工序使用总时差的方式具有更高的使用效率.文章随后对这一结论进行了科学性证明,并根据这个结论提出了项目管理中一种运用自由时差节约成本的方法,这种方法能帮助项目管理者提高机动时间使用效率.     

改进的CATSMLP预警藻类污染

人工神经网络由于其很多的特点与优势现已被广泛关注和运用.但是人工神经网络也存在学习过程易陷入局部极小、易出现震荡和网络存在冗余连接或节点等缺陷.针对这些不足,一种新的级联M LP神经网络CATSM LP比ATSM LP有更好的鲁棒性和高度的解释性,并且是一个万能逼近器.采用粒子群优化算法对其进行优化使其鲁棒性增强,具有更快速的收敛能力和更好的寻优能力,从而能更有效的建模.藻类的生长是湖泊等水体污染程度的一个直接表现形式.在某些情况下,甚至精密仪器都不能测出某些藻类污染物,因此需要好的方法越来越受到专家学者们的重视.将其用于藻类污染预警,仿真试验表明其用于环境污染防治有很好的效果,值得推广应用.     

滚装船在波浪中横摇时船上滑动重载荷的同步效应

由于波浪和内部滑动车辆共同作用，使滚装船的横摇加剧，这是许多滚装船发生倾覆的重要原因之一，对由滚装船和多辆滑动车辆组成的浮基多体系统，取滚装船的横摇角和多辆自由滑动车辆在甲板上的横向位移为此系统的自由度，通过对船舶在波浪中所受表观重力和表观浮力的分析，导出波浪作用力矩，运用多体系统动力学方法，建立了系统的动力学方程．以某型海峡滚装渡轮为例，对在多辆车自由滑动和波浪共同作用下的滚装船浮基多体系统的横摇响应和车辆位移响应进行了数值计算，得出了多个自由滑动的重载荷因相互碰撞在舷侧舱壁的约束下随着时间的延长其运动将趋于同步的结论．     

具有功能反应的污染环境中的非自治捕食系统的生存与灭绝

研究了一类具有HollingII型功能反应且居于污染环境中的非自治捕食系统,考虑到资源存在及死亡个体体内毒素回归环境对种群密度的影响.运用比较定理及微分方程稳定性理论,得到了此系统持续生存和灭绝的充分条件.     

一类非线性抛物型方程解的稳定性与唯一性

本文运用能量积分的方法，研究了一类非线性抛物型方程的解关于自由项与初始条件的稳定性与唯一性。     

广义弹塑性梁理论及接触问题中的时偶变分不等式

为研究摩擦接触问题，本文建立了一个具有二类独立交量的二维弹塑性梁模型。由此提出了一个新的非线性二次互补性问题．其中的外部互补性条件定义了自由边界；而内部互补性条件则控制了弹塑性分界面．文中证明了此二次互补性问题等价于一非线性变分不等式，并导出了其对偶变分不等式．本文结果显示对偶问题较原问题有更多的优越性．应用于塑性极限分析理论中，文中最后证明了一个简单的下限定理．     

Large Time Step Roe scheme for a common 1D two-fluid model

We present the Large Time Step (LTS) extension of the Roe scheme and apply it to a standard two-fluid model. Herein, LTS denotes a class of explicit methods that are not limited by the CFL (Courant–Friedrichs–Lewy) condition, allowing us to use very large time steps compared to standard explicit methods. The LTS method was originally developed in the nineteen eighties (LeVeque, 1985), where the Godunov scheme was extended to the LTS Godunov scheme. In the present work, the relaxation of the CFL condition is achieved by increasing the domain of dependence. This might lead to difficulties when it comes to boundary and source terms treatment. We address and discuss these difficulties and propose different ways to treat them. For a shock tube test case, where there are neither source terms nor difficulties associated with the boundaries, the method increases both accuracy and efficiency. For a water faucet test case that includes a source term, the method increases the efficiency, while the accuracy strongly depends on the appropriate treatment of boundary conditions and source terms.     

非凸单个守恒律初边值问题的整体弱熵解的构造

本文研究具有两段常数的初始值和常数边界值的非凸单个守恒律的初边值问题.在流函数具有一个拐点的条件下,由相应的初始值问题弱熵解的结构和Bardos-Leroux-Nedelec提出的边界熵条件,给出初边值问题整体弱熵解的一个构造方法,澄清弱熵解在边界附近的结构.与严格凸的单个守恒律初边值问题相比,非凸单个守恒律初边值问题的弱熵解中包括下列新的相互作用类型:一个接触或非接触激波碰到边界,边界弹回一个非接触激波.     

干旱区湖泊水质预测的数学模型

本文建立了干旱区湖泊水质的非线性数学模型 ,我们考虑了湖水的强烈蒸发因素 ,给出了适合干旱区的二维浅水湖的运动学方程组和污染物浓度场的扩散方程 ,作为水质分析的数学模型 ,对博斯腾湖两个典型水文年的矿化度浓度场进行了模拟计算 ,结果与实测值基本吻合 ,从而验证了该模型的准确性与可扩展性 .     

Determining the internal boundary of a region in the two-dimensional initial–boundary-value problem for the heat equation

The article investigates the reconstruction of the internal boundary of a two-dimensional region in the two-dimensional initial–boundary-value problem for the homogeneous heat equation. The initial values for the determination of the internal boundary are provided by a boundary condition of second kind on the external boundary and the solution of the initial–boundary-value problem at finitely many points inside the region. The inverse problem is reduced to solving a system of integral equations nonlinear in the function describing the sought boundary. An iterative numerical procedure is proposed involving linearization of integral equations.     

Uniqueness of analytic solutions for stationary plate oscillations in an annulus

The equations governing the harmonic oscillations of a plate with transverse shear deformation are considered in an annular domain. It is shown that under nonstandard boundary conditions where both the displacements and tractions are zero on the internal boundary curve, the corresponding analytic solution is zero in the entire domain. This property is then used to prove that a boundary value problem with Dirichlet or Neumann conditions on the external boundary and Robin conditions on the internal boundary has at most one analytic solution.     

Finite element modelling of surface waves in a channel

A variational formulation of the vertically-integrated differential equations for free surface wave motion is presented. A finite element model is derived for solving this nonlinear system of hydrodynamic equations. The time integration scheme employed is discussed and the results obtained demonstrate its good stability and accuracy.Several applications of the model are considered: the first problem is an open channel of uniform depth and the second an open channel of linearly varying depth. The ‘inflow’ boundary condition is prescribed in terms of the velocity which represents a wavemaker and/or a flow source, while the ‘outflow’ boundary condition is specified in terms of the water elevation. The outflow condition is adjusted for two cases, a reflecting boundary (finite channel) and a non-reflecting boundary (open-ended channel). The latter boundary condition is examined in some detail and the results obtained show that the numerical model can produce the non-reflecting boundary that is similar to the analytical radiation condition for waves. Computational results for a third problem, involving wave reflection from a submerged cylinder, are also presented and compared with both experimental data and analytical predictions.The simplicity and the performance of the computational model suggest that free surface waves can be simulated without excessively complicated numerical schemes. The ability of the model to simulate outflow boundary conditions properly is of special importance since these conditions present serious problems for many numerical algorithms.     

Finite element approximations to one‐phase nonlinear free boundary problem in groundwater contamination flow

In this article, we consider a single‐phase coupled nonlinear Stefan problem of the water‐head and concentration equations with nonlinear source and permeance terms and a Dirichlet boundary condition depending on the free‐boundary function. The problem is very important in subsurface contaminant transport and remediation, seawater intrusion and control, and many other applications. While a Landau type transformation is introduced to immobilize the free boundary, a transformation for the water‐head and concentration functions is defined to deal with the nonhomogeneous Dirichlet boundary condition, which depends on the free boundary function. An H¹‐finite element method for the problem is then proposed and analyzed. The existence of the approximation solution is established, and error estimates are obtained for both the semi‐discrete schemes and the fully discrete schemes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Quasihyperbolic boundary conditions and capacity: Hölder continuity of quasiconformal mappings

We prove that quasiconformal maps onto domains which satisfy a quasihyperbolic boundary condition are globally H?lder continuous in the internal metric. The primary improvement here over existing results along these lines is that no assumptions are made on the source domain. We reduce the problem to the verification of a capacity estimate in domains satisfing a quasihyperbolic boundary condition, which we establish using a combination of a chaining argument involving the Poincaré inequality on Whitney cubes together with Frostman's theorem. We also discuss related results where the quasihyperbolic boundary condition is slightly weakened; in this case the H?lder continuity of quasiconformal maps is replaced by uniform continuity with a modulus of continuity which we calculate explicitly. Received: June 16, 2000     

边界层问题的小波—有限元解

本文将小波分析与有限元法结合起来，建立了一种小波－有限元计算格式，并用该算法计算了一个典型的边界层问题，探讨了寻找边界层位置的过程以及计算边界层区的内部解及外部解的步骤。计算结果表明，用该法寻找的边界层位置以及所求得的内部解与真实结果完全符合。