一类积分不等式的机器判定

将一类积分不等式转化为Tarski模型外的齐次对称多项式不等式,该类齐次对称多项式的次数是给定的,变元个数可以是任意多个,并且多项式的系数是与变元个数相关的变系数.这些特点与杨路等人最近提出的几个公开问题密切相关,是比较有代表性的一类齐次对称多项式.然后利用Timofte关于对称多项式不等式判定的降维方法,结合不等式证明软件BOTTEMA及差分代换方法,给出对应的一类Tarski模型外的齐次对称多项式不等式的机器判定算法,从而实现原积分不等式的机器判定.当给定的积分不等式及齐次对称多项式不等式不成立时,可给出具体不成立的数值反例.应用例子表明问题的广泛性及算法的有效性.     

A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients

We propose a compact split-step finite difference method to solve the nonlinear Schrödinger equations with constant and variable coefficients. This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost. This method also preserves some conservation laws. Numerical tests are presented to confirm the theoretical results for the new numerical method by using the cubic nonlinear Schrödinger equation with constant and variable coefficients and Gross-Pitaevskii equation.     

Spectral element spatial discretization error in solving highly anisotropic heat conduction equation

This paper describes a study of the effects of the overall spatial resolution, polynomial degree and computational grid directionality on the accuracy of numerical solutions of a highly anisotropic thermal diffusion equation using the spectral element spatial discretization method. The high-order spectral element macroscopic modeling code SEL/HiFi has been used to explore the parameter space. It is shown that for a given number of spatial degrees of freedom, increasing polynomial degree while reducing the number of elements results in exponential reduction of the numerical error. The alignment of the grid with the direction of anisotropy is shown to further improve the accuracy of the solution. These effects are qualitatively explained and numerically quantified in 2- and 3-dimensional calculations with straight and curved anisotropy.     

New Riemannian techniques for directional and tensorial image data

This paper develops new geometrical filtering and edge detection algorithms for processing non-Euclidean image data. We view image data as residing on a Riemannian manifold, and we work with a representation based on the exponential map for this manifold together with the Riemannian weighted mean of image data. We show how the weighted mean can be efficiently computed using Newton's method, which converges faster than the gradient descent method described elsewhere in the literature. Based on geodesic distances and the exponential map, we extend the classical median filter and the Perona-Malik anisotropic diffusion technique to smooth non-Euclidean image data. We then propose an anisotropic Gaussian kernel for image filtering, and we also show how both the median filter and the anisotropic Gaussian filter can be combined to develop a new edge preserving filter, which is effective at removing both Gaussian noise and impulse noise. By using the intrinsic metric of the feature manifold, we also generalise Di Zenzo's structure tensor to non-Euclidean images for edge detection. We demonstrate the applications of our Riemannian filtering and edge detection algorithms both on directional and tensor-valued images.     

Anisotropic diffusion with generalized diffusion coefficient function for defect detection in low-contrast surface images

In this paper, an anisotropic diffusion model with a generalized diffusion coefficient function is presented for defect detection in low-contrast surface images and, especially, aims at material surfaces found in liquid crystal display (LCD) manufacturing. A defect embedded in a low-contrast surface image is extremely difficult to detect, because the intensity difference between the unevenly illuminated background and the defective region is hardly observable and no clear edges are present between the defect and its surroundings.The proposed anisotropic diffusion model provides a generalized diffusion mechanism that can flexibly change the curve of the diffusion coefficient function. It adaptively carries out a smoothing process for faultless areas and performs a sharpening process for defect areas in an image. An entropy criterion is proposed as the performance measure of the diffused image and then a stochastic evolutionary computation algorithm, particle swarm optimization (PSO), is applied to automatically determine the best parameter values of the generalized diffusion coefficient function. Experimental results have shown that the proposed method can effectively and efficiently detect small defects in various low-contrast surface images.     

基于综合匹配的鸟类视频中运动物体的检测

鄱阳湖是中国最大的湿地。每年秋末冬初,会有成千上万只候鸟来此越冬,该地区的自然生态系统和这些鸟类的活动有着密切的联系,因此,研究该地区的鸟类是了解该地生态系统的一个重要方式。本文采用帧间差分法对该地所拍摄鸟类视频数据进行运动物体检测。由于视频在获取过程中存在摄像机的移动,所以在处理过程中首先需要估计背景的运动并加以补偿。背景运动的估计是在常用的块匹配方法的基础上作了一定的改进,通过多个匹配块的匹配结果来计算运动矢量。为提高正确率,块的匹配在差分图像上进行。最后,利用在鄱阳湖录取的视频对本文所述方法进行了实验,实验结果表明本文所述方法对背景的去除和运动物体的检测的有效性。     

基于流场的爆炸分裂效果模拟

通过分析冲击波气流的运动特点,对Navier-Stokes方程进行合理简化。根据简化后的方程所反映出的气流速度变化规律,提出描述冲击波气流运动的扩散模型。基于该模型所定义的流场,对碎片的运动进行控制,实现对冲击波作用下物体碎片飞散效果的模拟。实验结果表明,该方法具有较强的真实感,能够满足实时性要求。     

国画水墨扩散的LBE计算机模拟

为了满足人们在美工设计中对计算机国画艺术效果仿真的需求,研究和分析了水墨扩散LBE(lattice Boltzmann equation,网格波尔兹曼)算法,提出运用亮度决定水粒子的初始分布,用CMY粒子进行扩散模拟.通过对LBE算法进一步推导而提出疑问,并对扩散及受阻方程进行修正.使用Wintab 1.1压感设备接口完成用户压感数据的读取,借助图像处理函数库IPL98 2.0进行扩散实验数据结构和实验流程设计,实现了国画水墨扩散效果的模拟,证明了该方法的可行性和有效性.     

基于人工神经网络的CCD数码相机颜色特征化

阐述了基于BP神经网络的数码相机特征化方法。采用不同的神经网络结构,建立了数码相机记录的RGB信息和原影像C IEXYZ色度信息之间的非线性对应关系。对NIKON D200数码相机进行了研究,通过实验得到了合理的神经网络结构为3—10—10—3。测试不同的训练样本和测试样本,达到的C IELAB平均色差和最大色差分别为1.9~2.2和6.7~7.4个色差单位。讨论了实验设备的重复性,同时,分析了样本数量对实验结果的影响。实验结果表明:对数码相机的特征化,可采用BP神经网络技术实现较高的精度。     

中国民间游戏和电子游戏的社会功能差异

游戏是一种古老的社会文化现象,自从有了人类就有了游戏。随着人类社会的发展、经济和科技水平的不断上升,游戏的概念和内涵也不再是跳皮筋、踢毽子等民间游戏活动。一种承载着更多经济、科技和文化内涵的游戏行为——电子游戏正在渗透到人们的生活中,人们认识到它更多的社会功能和价值,这种社会功能和价值因为游戏的内容、形式以及物质载体的巨大变化而形成了民间游戏和电子游戏的很大差异。