(3+1)维孤子方程的周期孤波解

扩展了Hirota法,即将Hirota法中的测试函数用新的测试函数来替代,并利用扩展了的方法来构造(3+1)维孤子方程的新的周期孤波解、周期双孤波解、双周期双孤波解.显然扩展的Hirota方法也可以解其他一些非线性发展方程.     

包含双温非热离子的尘埃等离子体中的三维尘埃声孤波

考虑高阶横向扰动的因素,使用约化摄动方法得到描述含有双温非热离子的无磁化尘埃等离子体中的尘埃声波的(3+1)维KP方程.详细讨论一些尘埃等离子体系统参数如电子与非热高温离子数密度v与μh、快离子数λ(α)、低温非热离子与电子的温度比β1、非热双温离子温度比β2对尘埃声孤波性质的影响.研究结果表明:这些因素均可显著影响和改变孤波结构.在考虑双温非热离子后,稀疏形孤波与压缩形孤波的临界条件也发生极大变化.     

非线性矩阵方程X-A*((X)-C)-n A=Q的正定解

研究了非线性矩阵方程X-A*((X)-C)-n A=Q的正定解,证明了该方程一定存在正定解,并给出了正定解的存在区间、存在唯一正定解的条件以及迭代求解方法.     

基于波能守恒方程模拟近岸波流场

基于波能守恒方程对平直斜坡上近岸波浪场以及近岸波浪斜向入射破碎后所产生的沿岸流场进行数值模拟.鉴于平直斜坡地形较简单,便于简单计算,利用基于波能守恒方程建立的波浪场数学模型计算得到波高的变化,从而利用Longuet-Higgins计算辐射应力.在此基础上,利用近岸波流场数学模型对实验波况下的波流场进行模拟,并将数值模拟结果与实验结果进行比较.结果表明,该模型可以很好地模拟近岸波流场.     

改进的tanh函数法在一类Fisher方程中的运用

利用改进的tanh函数法及齐次平衡法,借助Matlab的符号运算功能,构造并得到了一类Fisher方程的一些孤子解和一些三角函数解,并运用Matlab的三维绘图功能,得到了在特殊条件下的解的图像.     

洪水波泥石流防护对策研究

本文从洪水生成的技术基础研究出发,系统研究了溃坝洪水波理论方程及其涌浪激波问题的数值模拟方法,并对洪水波防护对策和措施进行归纳总结,结合工程实际提出了全国六大水系洪水波防护对策和措施的重大课题,期望对我国重要江河安全防护和我军履行抗洪抢险任务时的战略决策和防护对策有参考意义.     

谈有关超越方程根的常见题型

超越方程一般没有解析解,而只有数值解或近似解,只有特殊的超越方程才可以求出解析解来.求解超越方程的近似解法有很多,图象法虽然形象,但得到的解误差太大了.常用的近似解法有牛顿切线法、幂级数解法等等,现在也可以编制一段程序用计算机求解,或者利用现成的软件求解,例如大多数电脑都安装的EXCEL也可以用来求解超越方程.     

一类串联系统的边界Carleman估计

讨论了一类由两个热方程所组成的串联系统,在该串联系统中,将第一个方程的解作为第二个方程的边界输入,建立了解的边界Carleman型先验估计,即解在区域内部的加权L2模可以被解在部分边界上的加权L2模控制.     

一类多调和方程边值问题的可解性研究

多调和方程边值问题的研究是椭圆型偏微分方程边值问题研究的热点之一,本文通过引入新变量将多调和方程边值问题转换为椭圆型方程组问题,再利用Leray-Schauder不动点定理,证明了多调和方程边值问题解的存在性,同时,证明了一定条件下正解的唯一性,讨论了正解的不存在性.     

一类差分方程的解法及其在经济领域中的应用

差分方程模型是一种重要的确定性离散模型,其中较常用的有N阶常系数线性非齐次差分方程模型,用待定系数法解此类方程,研究此类方程在市场经济分析中的应用,给出蛛网模型的三阶差分模型.     

Multicomponent diffusion simulation based on finite elements

A numerical model is presented to treat multicomponent, multiphase diffusion problems. Unlike other recent approaches that are based on the finite-difference method, analytical solutions, or particular thermodynamic models, a general procedure based on the finite-element technique is applied. The suggested formalism is based on the solution of the integral statement of the generalized diffusion equation. This treatment allows for a simple implementation of particular boundary conditions and can easily be extended from a one- to a multidimensional analysis. A brief overview of the formal representation of multicomponent diffusion coefficients, as suggested by Andersson and Agren, is given. The finite-element diffusivity matrices are evaluated for a one-dimensional bar and a two-dimensional triangular element. The model is applied to some classical examples in diffusion simulation in both one and two dimensions. The results are compared to available analytical solutions or experimental data.     

Collection Conduits Including Subsurface Drains

Numerous types of pipes and channels with spatially increasing flows in environmental engineering applications are identified by type and function and referred to as collection conduits. An overview of methods for designing and analyzing collection conduits is provided. Full conduits with nonuniform and uniform inflow are first considered. Dimensional analysis is then employed to demonstrate the relationship between variables for open channels; that leads to the identification of possibilities for generalized numerical solutions. Prior collection conduit applications are discussed within the framework of the dimensional analysis (which also pertains to some constant-flow applications). A previously unpublished generalized numerical solution for rectangular collection conduits is presented. Subsurface drains are addressed with particular emphasis, including the use of numerical methods to develop a new generalized chart and relation to other design methods. Among the important conclusions for subsurface drains is that the somewhat common practice of using Manning’s equation alone for such problems is not generally adequate. Examples and practical design suggestions are included, and the use of computer-based numerical methods is discussed more generally.     

Roll Flattening Analytical Model in Flat Rolling by Boundary Integral Equation Method

In order to improve rolled strip quality, precise plate shape control theory should be established. Roll flattening theory is an important part of the plate shape theory. To improve the accuracy of roll flattening calculation based on semi-infinite body model, especially near the two roll barrel edges, a new and more accurate roll flattening model is proposed. Based on boundary integral equation method, an analytical model for solving a finite length semi-infinite body is established. The lateral surface displacement field of the finite length semi-infinite body is simulated by finite element method (FEM) and lateral surface displacement decay functions are established. Based on the boundary integral equation method, the numerical solution of the finite length semi-infinite body under the distributed force is obtained and an accurate roll flattening model is established. Different from the traditional semi-infinite body model, the matrix form of the new roll flattening model is established through the mathematical derivation. The result from the new model is more consistent with that by FEM especially near the edges.     

一类散度型椭圆方程弱解的最大模估计

研究了散度型椭圆方程的弱解的性质。利用De Giorgi迭代技术做出了比Poisson方程稍一般的方程的弱解的最大模估计。     

Provision of Reinforcement in Concrete Solids Using the Generalized Genetic Algorithm

A generalized genetic algorithm has been developed to find the global optimal reinforcement contents for a concrete solid structure subjected to a general three-dimensional (3D) stress field. Feasible solutions were examined based on the genetic algorithm, and the heterogeneous strategy used ensures that all of the local optimal regions are searched and the most optimal reinforcement content found. The effectiveness of the proposed approach has been validated by comparing the steel contents evaluated using the present method with those obtained from other available methods. A more economic design is achieved by the proposed algorithm. The method developed provides the designer with a valuable tool for the determination of reinforcements in complicated solid concrete structures.     

Exact Discontinuous Solutions of Exner’s Bed Evolution Model: Simple Theory for Sediment Bores

Determining the evolution of the bed of a river or channel due to the transport of sediment was first examined in a theoretical context by Exner in 1925. In his work, Exner presents a simplified bed evolution model derived from the conservation of fluid mass and an “erosion” equation that is commonly referred to as the sediment continuity or Exner equation. Given that Exner’s model takes the form of a nonlinear hyperbolic equation, one expects, depending on the given initial condition of the bed, the formation of discontinuities in the solution in finite time. The analytical solution provided by Exner for his model is the so-called classical or genuine solution of the initial-value problem, which is valid while the solution is continuous. In this paper, using the general theory of nonlinear hyperbolic equations, we consider generalized solutions of Exner’s classic bed evolution model thereby developing a simple theory for the formation and propagation of discontinuities in the bed or so-called sediment bores.     

Structural Equation Models of Latent Interactions: Evaluation of Alternative Estimation Strategies and Indicator Construction.

Interactions between (multiple indicator) latent variables are rarely used because of implementation complexity and competing strategies. Based on 4 simulation studies, the traditional constrained approach performed more poorly than did 3 new approaches-unconstrained, generalized appended product indicator, and quasi-maximum-likelihood (QML). The authors' new unconstrained approach was easiest to apply. All 4 approaches were relatively unbiased for normally distributed indicators, but the constrained and QML approaches were more biased for nonnormal data; the size and direction of the bias varied with the distribution but not with the sample size. QML had more power, but this advantage was qualified by consistently higher Type I error rates. The authors also compared general strategies for defining product indicators to represent the latent interaction factor. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential

In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the Lp type estimates and the theory of Morrey spaces, we prove the HSlder continuity of the solutions. Then we obtain the existence of global classical solutions. The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.     

Vertical and Radial Consolidation Analysis of Multilayered Soil Using the Spectral Method

A new, easy to implement, solution to the consolidation of multilayered soil based on the spectral method is presented. Combined vertical and radial drainage under instantaneous or single ramp loading is considered, ignoring well resistance. Flow in the vertical direction is based on the average hydraulic gradient at a particular depth which allows smear effects to be included. The excess pore-water pressure profile across all soil layers is described by a single expression calculated with common matrix operations. Average excess pore pressures within or across any number of layers are easily calculated from the single expression. The new model is verified against other solutions from the current literature indicating that the more general spectral method model can replace the separate solutions developed for specific problems.     

Predictors of Chlamydia trachomatis infection among female adolescents: a longitudinal analysis

Screening guidelines recommend testing all sexually active female adolescents for Chlamydia trachomatis during a pelvic examination at each clinic visit. Such criteria have been based on cross-sectional studies; new evaluations should take into account multiple clinic visits and assess whether criteria are appropriate when a prior test is negative and risk factors are absent. Because repeated observations on an individual may be correlated, the authors used the generalized estimating equation method. Little information exists on subsequent risk of infection; as control programs develop, approaches targeting high-risk populations for recurrent infections are needed. Using data on females aged 15-19 years who visited family planning clinics more than once from 1988 to 1992 (n = 26,921) in Region X (Alaska, Idaho, Oregon, and Washington), the authors constructed a retrospective cohort. Teens with chlamydia at their first visit were at high risk for subsequent infection (odds ratio = 1.6, 95% confidence interval 1.4-1.7). Among teens uninfected at the first visit and without risk factors at the second, prevalence at the second visit was 6%. When intervisit correlations using the generalized estimating equation method were taken into account, predictors of chlamydial infection were consistent with those in previous cross sectional studies cervicitis, friable cervix, and multiple, new, or symptomatic sex partner(s). These findings support screening sexually active female adolescents at each visit, even if prior tests results are available.