各向异性板弯曲的积分方程

推导了一般各向异性板弯曲的积分方程,此积分方程适用于各类边界条件.并对积分方程作了离散化,提出了解法.     

近表面洞室对矢量波散射问题的边界元解

采用无限边界元方法研究了半空间中一近表面洞室对矢量波的散射问题,给出了以全空间格林函数为基本解且半空间表面离散的边界积分方程．在这一边界积分方程中,较好地消除了主值积分．在半空间表面进行离散时,采用无限单元与有限单元相结合的方法,大大减少了计算量,提高了精度．     

分数阶Cauchy问题解的离散化逼近

作者研究了Laplace变换的离散逼近,讨论了分数阶Cauchy问题解的离散化逼近,并分别给出了在α∈ (0,1)和α∈［1,2)时不同的逼近定理.     

New method for discretization of continuous attributes in rough set theory

A new method for discretization of continuous attributes is put forward to overcome the limitation of the traditional rough sets,which cannot deal with continuous attributes.The method is based on an improved algorithm to produce candidate cut points and an algorithm of reduction based on variable precision rough information entropy.With the guarantee of consistency of decision system,the method can reduce the number of cut points and improve efficiency of reduction.Adopting variable precision rough information entropy as measure criterion,it has a good tolerance to noise.Experiments show that the algorithm yields satisfying reduction results.     

求解Hamilton-Jacobi方程的一类高精度差分格式

构造了一、二维非线性Hamilton-Jacobi方程的一类新的高精度高分辨率差分格式.首先将计算区域划分为互不重叠的子单元,再根据格式的精度要求分割子单元为细小于单元,其次通过子单元上各个细小子单元节点的函数值构造空间导数的高阶插值逼近,为避免由此产生的数值振荡,对空间导数在各节点左右侧的值进行TVD/TVB校正,利用高阶Runge-Kutta TVD时间离散方法得到一维Hamilton-Jacobi方程的高阶全离散格式并推广到二维情况,最后给出了几个典型的数值算例,验证了格式具有计算简单、高分辨间断导数、无振荡等特性.     

Half-global discretization algorithm based on rough set theory

It is being widely studied how to extract knowledge from a decision table based on rough set theory. The novel problem is how to discretize a decision table having continuous attribute. In order to obtain more reasonable discretization results, a discretization algorithm is proposed, which arranges half-global discretization based on the correlational coefficient of each continuous attribute while considering the uniqueness of rough set theory. When choosing heuristic information, stability is combined with rough entropy. In terms of stability, the possibility of classifying objects belonging to certain sub-interval of a given attribute into neighbor sub-intervals is minimized. By doing this, rational discrete intervals can be determined. Rough entropy is employed to decide the optimal cut-points while guaranteeing the consistency of the decision table after discretization. Thought of this algorithm is elaborated through Iris data and then some experiments by comparing outcomes of four discritized datasets are also given, which are calculated by the proposed algorithm and four other typical algorithms for discritization respectively. After that, classification rules are deduced and summarized through rough set based classifiers. Results show that the proposed discretization algorithm is able to generate optimal classification accuracy while minimizing the number of discrete intervals. It displays superiority especially when dealing with a decision table having a large attribute number.     

基于断点辨别力的粗糙集离散化算法

提出了基于断点辨别力的粗糙集离散化算法.通过分析候选断点与决策类之间的相关性,定义了候选断点对决策类的辨别力,并以此作为断点重要性的度量,实现连续属性的离散化.离散化后的决策系统不改变原有的相容性,而且能最大限度地保留有用信息.采用多组数据对该算法的性能进行了检验,并与其它算法做了对比实验实验结果表明该算法是有效的,而且当候选断点个数增多时仍具有较高的计算效率.     

序列运算离散化过程中的误差成因及补偿

为了减少序列离散化过程导致的误差,提出几种概率补偿的方法。由误差的成因入手,分析了离散化过程的误差机理,将利用随机变量的概率分布函数离散化后所得序列,分别以修正公式、平均补偿法及比例补偿法进行补偿,推导出各种误差补偿方法下序列期望值及方差的误差估计公式。结果表明:经误差补偿后,算例中序列期望值误差下降为原误差的8%以下,而方差误差至少可降为原误差的91%。     

一种基于条件熵的粗糙集连续属性离散化方法

连续属性离散化是粗糙集应用研究的重点内容之一.基于条件熵可以反应属性依赖度的性质,将决策属性对条件属性的条件熵作为离散化标准,提出了一种粗糙集连续属性离散化方法,并通过实例证明了该方法的正确性.     

车灯线光源的优化及其Matlab实现与仿真

利用离散化的思想,将线光源离散为点光源,将反射抛物面离散为抛物面上一条螺旋形曲线上一系列的点,成功地解决了距离25 m远处测试屏上直射光线和反射光线形成的面积问题,并实现了基于Matlab的仿真.仿真结果与理论吻合.通过具体事例,揭示了在数学建模过程中离散化思想的运用以及利用Matlab实现与仿真的优势.