Uncertainty of the numerical solution of a nonlinear system’s long-term behavior and global convergence of the numerical pattern

The computational uncertainty principle in nonlinear ordinary differential equations makes the numerical solution of the long-term behavior of nonlinear atmospheric equations have no meaning. The main reason is that, in the error analysis theory of present-day computational mathematics, the non-linear process between truncation error and rounding erroris treated as a linear operation. In this paper, based on the operator equations of large-scale atmospheric movement, the above limitation is overcome by using the notion of cell mapping. Through studying the global asymptotic characteristics of the numerical pattern of the large-scale atmospheric equations, the definitions of the global convergence and an appropriate discrete algorithm of the numerical pattern are put forward. Three determinant theorems about the global convergence of the numerical pattern are presented, which provide the theoretical basis for constructing the globally convergent numerical pattern. Further, it is pointed out that only a globally convergent numerical pattern can improve the veracity of climatic prediction.     

基于模糊逻辑T算子和协T算子的地下水水质评价

本文运用地下水水质的模糊综合评判分析方法，选取地下水水质的主要影响因子，借助模糊逻辑T算子和协T算子，编制了有效的MATLAB计算机程序，绘制了隶属度函数的数学图形，对北方某水源地地下水水化学资料进行了模糊数学综合评价。评价结果表明，研究区采样点水质为Ⅰ、Ⅱ、Ⅲ级的占96．63％，大部分地下水水质较好，符合饮用水的要求。借助T和协T逻辑算子的模糊综合评判法评价地下水水质效果较好。     

点特征提取算法探讨

影像特征提取是影像匹配和三维信息提取的基础,是影像分析与单像处理技术领域中最重要的任务之一。有效的特征提取算法是影像分析与处理的关键。从点特征定义出发,叙述了两种常用的点特征提取算子---Moravec算子和Forstner算子的原理,利用Moravec算子和Forstner算子可以实现影像点特征的提取,并从提取点特征的准确度、提取速度对两种算子进行比较,最后得出了有益的结论。     

基于Canny理论的彩色图像边缘检测

选用定位准确的Canny算子,提出一种基于Canny理论的彩色图像边缘检测方法。彩色图像的梯度幅值用其r、g、b分量的梯度幅值之和计算,方向角用r、g、b分量的y方向梯度幅值之和与r、g、b分量的x方向梯度幅值之和的比来确定。从检测结果中可以看出,基于Can-ny理论的彩色图像边缘检测能检测出更多的边缘细节。这说明,用该方法检测彩色图像的边缘是有效的。     

GIS中统一于Qi算子的多边形基本问题新算法

用Qi算子来描述多边形中边和连线两类矢量的方向角，归纳出由Q算子所表示的矢量方向角在识别走向时的判断规则，从而成功建立了多边形4个基本问题的新算法。实现了4个算法在几何意义上的统一，并相对传统最优算法提高了执行效率，同时还保证了高可靠性和稳定性。     

小波多尺度影像边缘聚焦算法

讨论了基于光滑函数的二维小波极大模边缘算子和小波过零点边缘算子及其特性。提出了多尺度二进小波变换过零点边缘聚焦算法。通过对不同尺度下小波变换的遥感影像进行复合、边缘提取和聚焦后结果进行比较，可以发现该算法适应影像空间尺度不确定性目标边缘提取。既可保证大尺度下的轮廓信息不失真，又能在边缘定位上保持很高的精度。     

Marr方法在多波段遥感影像边缘信息分析中的应用

简要介绍了Marr理论的基本框架，并详细介绍了Marr-Hildreth边缘检测理论的基本原理，同时给出了LOG模板算子实例。在此基础上，提出这一理论用于多波段影像边缘分析的几种不同的方法，指出了本文所采取方法的原理和算法流程。试验结果的分析对比说明，多波段影像分析的效果优于单波段。     

THE EFFECTS OF EXTERNAL FORCING,DISSIPATION AND NONLINEARITY ON THE SOLUTIONS OF ATMOSPHERIC EQUATIONS

Based on the primitive equations of the atmosphere,we study the effects of external forcing.dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.Theresults show that the asymptotic behavior of solutions of the forced dissipative nonlinear system isessentially different from that of the adiabatic non-dissipative system,the adiabatic dissipativesystem,the diabatic non-dissipative system and the diabatic dissipative linear system,and that thejoint action of external forcing,dissipation and nonlinearity is the source of multiple equilibria.From this we can conclude that the important actions of diabatic heating and dissipation must beconsidered in the models of the long-term weather and the climate.     

On the control of an infinite capacity storage system

We consider an infinite-capacity storage system. The cumulative input to the system is assumed to be either (a) a non-decreasing Lévy process or (b) an integrated continuous-time Markov chain. Reward accumulates at a rate depending on the instantaneous release rate. The objective is to choose the release rule in such a way as to maximize the expected total discounted return. In this note we show how to determine the expected discounted return when the release rate is either constant or a linear function of the content.     

分数微分积分及其级数展开式

用积分算子定义分数微分和分数积分,给出分数微分积分的级数展开式,并介绍分数微分积分的数值计算。