全局最优化的平滑积分变换方法Ⅰ基本思想和理论框架

提出了解决全局最优化中多极小问题的平滑积分变换方法．通过平滑积分变换将目标函数平滑变形，充分变形后的目标函数将仅有一个极小，沿该极小在变形过程中的轨迹回溯即可找出其对应的原始目标函数的一个较深且较宽的极小．研究了平滑积分变换的数学性质并提出了不依赖局部极小化算法的极小追踪技术．     

导数分光光度测定中的计算机图形分析

应用计算机图形分析技术结合普通分光光度计进行导数分光光度法的测定。给出了计算机曲线光顺，拟合等算法以及导数分光光度测定的计算机图形分析程度“ＵＶ－ＤＳ”和回归分析程序“ＵＶ－ＨＧ”工作框图。采用本方法，以盐酸麻黄碱滴鼻剂为例，使用“ＵＶ－ＤＳ”程序，给出了盐酸麻黄碱和干扰组分尼泊金乙酯的各阶导数光谱曲线图以及测定参数，完成了含量的测定。     

一种改进的图像自适应非线性滤波方法

针对图像的保边光滑问题，分析了Perona-Malik(PM)方程的非线性滤波扩散行为，利用保边正则化思想给出了由一种新的各向异性扩散方程所决定的图像自适应光滑算法。这种新的各向异性扩散滤波方法与PM方程的不同之处在于：扩散系数不是直接来源于图像的梯度幅值，而是在图像梯度模基础上恢复出图像的边缘信息。实验结果表明，所提方法对图像边缘的恢复结果要比PM的方法具有更高的可靠性和准确性。     

数字图像的平滑

一幅原始图像，在获取和传输过程中，会受到各种噪声的干扰，使图像退化，质量下降．退化会引起图像模糊，特征淹没，对分析图像不利．为了抑制噪声改善图像质量进行的处理称为图像平滑或去噪．数字图像平滑处理可以在空间域或频率域中进行．分析图像平滑处理方法，对相关方法的适用场合进行探讨，并且给出实现程序．     

非线性l1 问题的光滑近似算法

利用“ ”函数的光滑近似函数和无约束优化方法给出非线性l1的一种算法．在适当的假设下，算法是全局收敛的．初步的数值试验结果表明算法的有效性．     

抗污染攻击的流内安全网络纠错编码

传统的网络路由并不能达到多播网络中"最大流-最小割"定义的Shannon容量限,而网络编码很好地解决了上述问题,在增大吞吐量的同时还可以均衡网络负载,提高带宽利用率.但是当网络中存在恶意攻击时会引入错误数据包,在线性网络编码操作下会带来数据包的"错误扩散",不仅影响网络性能,还会造成资源的严重浪费.因此如何在优化网络传输性能的同时提高通信网络的安全性成为目前亟待解决的问题.本文采用基于同态校验的线性网络纠错编码机制进行差错控制,拟解决多播网络中的污染攻击问题,对安全性能以及传输性能进行了分析.仿真结果表明基于同态校验的网络纠错编码能够在不破坏数据包编码规则的前提下及时地进行错误的检测和纠正,得到较好的差错控制性能,能够对抗网络中恶意节点引起的污染攻击问题.      

基于组合预测模型在高校招生人数预测中的应用研究

引进诱导有序加权平均算子,建立诱导有序加权平均组合预测模型,借助它对四川省普通高等学校招生人数进行预测.通过两个误差指标值的比较,说明这种方法的合理性,从而为教育部门制定相关的就业体制提供依据.     

Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms

Explicit and partly sharp estimates are given of integrals over the square of Bessel functions with an integrable weight which can be singular at the origin. They are uniform with respect to the order of the Bessel functions and provide explicit bounds for some smoothing estimates as well as for the L² restrictions of Fourier transforms onto spheres in which are independent of the radius of the sphere. For more special weights these restrictions are shown to be Hölder continuous with a Hölder constant having this independence as well. To illustrate the use of these results a uniform resolvent estimate of the free Dirac operator with mass in dimensions is derived.     

A three‐dimensional Cartesian cut cell method for incompressible viscous flow with irregular domains

A three‐dimensional Cartesion cut cell method is presented for the simulations of incompressible viscous flows with irregular domains. A new model (referred to as ‘6+N’ model) is proposed to describe arbitrarily shaped cut cells and treat all the cells as polyhedrons with 6+N faces. The finite volume discretization of the Navier–Stokes equation is then implemented by using the ‘6+N’ model to separate the surface flux integrals into two parts, that is, the fluxes through the basic face of the hexahedron and those through the cutting surfaces. The previously proposed Kitta Cube algorithm and volume computer‐aided design platform (J. Comput. Aided. Des. 2005; 37(4): 1509–1520. Doi:10.1016/j.cad.2005.03.006) are adopted to generate cut cells and provide shape data and physical attributes for the numerical analysis. A modified SIMPLE‐based smoothing pressure correction scheme is applied to suppress checkerboard pressure oscillations caused by the collocated arrangement of velocities and pressure. The calculation accuracy of the numerical method expressed by L₁ and L _∞ norm errors is first demonstrated by the simulation of a pipe flow. Then its feasibility, efficiency, and potential in engineering applications are verified by applying it to solve natural convections between concentric spheres and between eccentric spheres. The heat transfer patterns in eccentric spheres are also obtained by using the numerical method. Copyright © 2011 John Wiley & Sons, Ltd.