An analytical and numerical study of the two-dimensional Bratu equation

Bratu's problem, which is the nonlinear eigenvalue equationu+ exp(u)=0 withu=0 on the walls of the unit square and as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance ofsymmetry: because of invariance under the C₄ rotation group and parity in bothx andy, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral method is ananalytical as well as a numerical tool: the simple approximation3.2A exp(–0.64A), whereA is the maximum value ofu(x, y), is derived via collocation with but a single interpolation point, but is quantitatively accurate for small and moderateA. Third, the Newton-Kantorovich/Chebyshev pseudospectral algorithm is so efficient that it is possible to compute good numerical solutions—five decimal places—on amicrocomputer inbasic. Fourth, asymptotic estimates of the Chebyshev coefficients can be very misleading: the coefficients for moderately or strongly nonlinear solutions to Bratu's equations fall off exponentially rather than algebraically withv untilv is so large that one has already obtained several decimal places of accuracy. The corner singularities, which dominate the behavior of the Chebyshev coefficients in thelimit v, are so weak as to be irrelevant, and replacing Bratu's problem by a more complicated and realistic equation would merely exaggerate the unimportance of the corner branch points even more.     

冲压件CAPP系统中几何信息提取实现

基于对AutoCAD的DXF文件格式的详细分析，充分利用多义线的表达简洁性优点，并结合冲压件自身特点，提出了冲压件几何信息获取的方法及程序框架，详细说明了几何信息库的创建方法，并进一步采用Delphi6．0语言编程，实现了冲压几何信息库的建立和几何信息自动提取。     

广义线性模型与非线性模型参数的统计推断

概述了广义线性模型(含半参数广义线性模型)与非线性模型研究的新进展,着重讨论了它们参数估计的统计推断。近年来,广义线性模型与非线性模型的研究发展迅速,有着广泛的应用前景。     

Consistent hierarchical economic NMPC for a class of hybrid systems using neighboring-extremal updates

A hierarchical two-layer control algorithm is developed for a class of hybrid (discrete-continuous dynamic) systems to support economically optimal operation of batch or continuous processes with a predefined production schedule. For this class of hybrid systems, the optimal control moves as well as the controlled switching times between two adjacent modes are determined online. In contrast to closely related schemes for integrated scheduling and control, the sequence of modes is not optimized. On the upper layer, the economic optimal control problem is solved rigorously by a slow hybrid economic model predictive controller at a low sampling rate. On the lower layer, a fast hybrid neighboring-extremal controller is based on the same economic optimal control problem as the slow controller to ensure consistency between both layers. The fast neighboring-extremal controller updates rather than tracks the optimal trajectories from the upper layer to account for disturbances. Consequently, the fast controller steers the process to its operational bounds under disturbances and the economic potential of the process is exploited anytime. The suggested two-layer control algorithm provides fully consistent control action on the fast and slow time-scale and thus avoids performance degradation and even infeasibilities which are commonly encountered if inconsistent optimal control problems are formulated and solved.     

多维超几何分布的最可能成功数

超几何分布是一种重要的离散型概率分布,本文利用反证法以及比较法求出了三维超几何分布的最可能成功次数,并在此基础上,求出了多维超几何分布的最可能成功次数.     

梁端翼缘扩大型梁柱节点抗震性能和设计方法

为使钢框架梁柱节点满足强柱弱梁的抗震设计原则,并使梁上塑性铰远离梁柱节点区,对梁端翼缘扩大型(包括侧板加强型和翼缘端部放大型)钢框架梁柱节点进行了往复荷载下的试验研究,得到了节点类型和梁端翼缘扩大尺寸对节点滞回性能、延性和耗能能力等指标的影响规律.在使用非线性有限元程序对试验结果进行数值模拟的基础上,研究了梁端翼缘扩大段的长度及宽度等参数对节点性能的影响规律和有效取值范围,给出了实用设计方法.使用梁端翼缘扩大型钢框架节点可以有效实现梁端塑性铰外移,是一种在抗震设计中值得推广的具有良好延性和塑性转动能力的新型节点形式.     

给水处理投药控制的非线性数学模型及仿真

为了更好地控制给水处理系统中的投药量,本文用机理建模及分布参数系统建模的方法,建立了可用于给水处理投药过程控制的数学仿真模型,该仿真模型包括了给水处理过程中混凝、絮凝、沉淀3步最基本过程,反映了水厂各设计参数对水处理投药控制效果的影响以及混凝药剂与絮凝池、沉淀池出水浊度之间的动态响应关系.仿真模拟了水厂原水浊度发生突变对絮凝池及沉淀池的出水浊度的动态影响,仿真结果与实际水厂数据相近.研究结果可以用来进一步研究水处理过程控制,为更深入研究适用于给水处理的非线性控制方法提供良好的模拟仿真分析平台.     

电路模拟中非线性方程的周期波形响应

用范数估计方法对非线性高阶微分方程的周期边值问题进行了讨论,通过对非线性二阶微分方程周期边值问题的详细讨论,给出了系统函数对某些变量偏导数的某种范数小于1时,非线性二阶微分方程的波形松弛算法产生的迭代序列收敛到该方程的周期解.用类似的方法给出了非线性高阶微分方程的波形松弛算法产生的迭代序列收敛到该方程周期解的充分性条件.     

通用突变控制方法及其在潜艇中的应用

运用非线性动力学和突变理论,研究了高维系统建立具有理想特性突变的控制方法.引入冲失滤波器保证系统平衡点不变,并利用隐式判据、中心流形定理以及规范形法确定控制增益.以潜艇空间运动为例,阐述计算的全过程.该控制方法简便、快捷,可广泛应用到实际控制系统的设计中.     

四叔丁基萘酞菁氧钒非线性及光限幅特性

为提高酞菁化合物的非线性光学性能,以1,8-二氮杂双环[5.4.0]十一碳烯-7(DBU)为催化剂,采用液相法合成了四叔丁基萘酞菁氧钒((t-Bu)4NcVO)化合物.利用元素分析、红外光谱、核磁共振氢谱方法,验证了化合物的分子结构.应用调Q倍频ns/ps Nd∶YAG脉冲激光系统,在波长为532nm下,研究了化合物的非线性和光限幅特性.测得化合物的非线性折射率n2和三阶非线性极化率χ(3)分别为2.51×10-11esu和8.54×10-12esu,通过计算得到分子极化率γ’为3.7×10-29esu.在透过率69%时限幅阈值为1608mJ/cm2,箝位值为585mJ/cm2,有效激发态与基态吸收截面比为3.66.