电磁领域中复超越方程的遗传算法求解方法

将遗传算法与参数跟踪策略有效结合,跟踪过程中进行搜索域压缩与位移操作,形成了一种功能强大的新算法,可成功应用于电磁领域中各种各样复超越方程的高精度求解问题.在算法实现过程中,使用参数跟踪策略有效地缩小了搜索区域,保证了解的单一性,提高了运算速度;使用动态搜索域提高了解的精度;应用三阶差商公式预估新的搜索中心,使运算速度得以进一步提高.应用本文发展的算法详细求解了终端短路法测量材料的复介电常数时得到的复超越方程和部分填充矩形波导的特征方程,计算结果表明该算法能够轻松地解决复超越方程中的多值问题,解集完备性好,算法鲁棒性强.     

广义KDV-MKDV方程的精确解

利用直接积分方法将广义KDV-MKDV方程化为一阶变系数非线性常微分方程组,然后用待定系数法确定相应的常数获得了广义KDV-MKDV方程新的精确解;利用先作假设变换后选取试探函数的方法来直接构造广义KDV-MKDV方程新的精确解.     

脉冲微分方程理论在药物动力学中的应用研究

为了揭示药物在机体内的ADME过程,将脉冲微分方程理论应用于研究药物动力学若干问题中,通过对系统动力学行为的研究进而设计最佳用药方案,丰富了脉冲微分方程理论并对指导临床实践具有积极意义.     

小波变换在求解重力测定反问题中的应用

针对重力测定反问题,提出将其离散为线性不适定问题,利用小波变换方法进行数值求解.该方法将小波变换和正则化方法相结合,选取小波函数作为一组基底,将原不适定问题转化为粗子空间上的适定问题,并给出选取粗子空间基的方法.通过数值模拟已有方法和小波变换方法求解结果的比较,表明了小波变换方法的可行性和有效性.     

高维力学系统的能量方程

在低维系统中,能量方程因其明晰的物理意义而得到广泛的应用,而研究高维力学系统的能量方程也同样具有理论价值和实际意义,如位移对时间的导数是速度,速度对时间的导数是加速度,这些具有明显的物理意义,而加速度的导数其物理意义就不是很清晰了,但具有理论上的意义.本文应用广义经典力学中关于广义拉格朗日函数、广义动量和广义哈密顿函数等概念,推导了高维系统的能量方程,文中举了实例具体说明新方程的应用,为力学数学系统能量方程的推广提供了一种途经.     

A macro-meso constitutive law for concrete having imperfect interface and nonlinear matrix

The overall behavior of concrete depends on its meso structures such as aggregate shape, interface status, and mortar matrix property. The two key meso structure characters of concrete, bond status of interface and nonlinear property of matrix, are considered in focus. The variational structure principle is adopted to establish the macro-meso constitutive law of concrete. Specially, a linear reference composite material is selected to make its effective behavior approach the nonlinear overall behavior of concrete. And the overall property of linear reference composite can be estimated by classical estimation method such as self-consistent estimates method and Mori-Tanaka method. This variational structure method involves an optimum problem ultimately. Finally, the macro-meso constitutive law of concrete is established by optimizing the shear modulus of matrix of the linear reference composite. By analyzing the constitutive relation of concrete established, we find that the brittleness of concrete stems from the imperfect interface and the shear dilation property of concrete comes from the micro holes contained in concrete. Supported by the National Natural Science Foundation of China (Grant Nos. 50679022, 90510017, 50539090) and National Basic Research Program of China (Grant No. 2007CB714104)     

Fractional partial differential equation denoising models for texture image

In this paper,a set of fractional partial differential equations based on fractional total variation and fractional steepest descent approach are proposed to address the problem of traditional drawbacks of PM and ROF multi-scale denoising for texture image.By extending Green,Gauss,Stokes and Euler-Lagrange formulas to fractional field,we can find that the integer formulas are just their special case of fractional ones.In order to improve the denoising capability,we proposed 4 fractional partial differential equation based multiscale denoising models,and then discussed their stabilities and convergence rate.Theoretic deduction and experimental evaluation demonstrate the stability and astringency of fractional steepest descent approach,and fractional nonlinearly multi-scale denoising capability and best value of parameters are discussed also.The experiments results prove that the ability for preserving high-frequency edge and complex texture information of the proposed denoising models are obviously superior to traditional integral based algorithms,especially for texture detail rich images.     

组合KdV方程的Hamilton系统

本文根据KdV方程的Hamilton系统,构造并证明了组合KdV方程的Hamilton系统。     

受强弱关系理论启发的改进人工蜂群算法

针对原人工蜂群算法在寻优过程中存在收敛精度不高、容易陷入局部最优的问题,提出一种改进人工蜂群算法(SWT-ABC)。将社会学中强弱关系模型化并引入多子群矩阵式蜂群结构,定义了强关系个体从三个方向随机引导搜索,加快算法收敛速度和提高收敛精度;为增强算法跳出局部最优的能力,定义了弱关系个体交互以实现子群间信息交流来提升种群多样性;增加侦查蜂反向学习机制并确定合适的蜜源上限,能有效提升目标函数评价次数的利用效率。通过基准测试函数的数值实验并与12种改进算法进行对比,改进后的人工蜂群算法收敛精度更高、全局寻优能力更强,并且在高维优化问题求解中仍具备良好的收敛性能。     

基于反应扩散方程的水平集结构拓扑优化方法与实现

为实现更加先进的拓扑优化算法,研究采用反应扩散方程的水平集结构拓扑优化方法,通过理论推导给出算法中的参数选择建议.该方法允许在拓扑优化过程中生成新的孔洞,初始结构无须包含孔洞,不需要重新初始化步骤,从而可提高算法的收敛性.针对传统拓扑优化中主要采用体积约束、以柔度最小为目标和体积保留率设定存在一定主观性的问题,探究不同体积保留率下的结构应力水平的变化规律,结果显示可以依据结构最大应力水平与体积保留率的变化规律确定最优体积保留率.