Benjamin-Bona-Mahony方程的平均隐式差分格式

本文对Benjamin-Bona-Mahony(BBM)方程的初边值问题进行了数值研究,提出了一个平均隐式差分格式,讨论了差分解的存在唯一性.然后利用离散泛函分析方法分析了该格式的二阶收敛性与稳定性,然后利用数值实验进行了验证.     

二维液晶环型光子晶体的可调完全带隙

利用平面波展开法研究了二维三角晶格液晶环型光子晶体的完全带隙的动态可调节性.数值模拟结果表明:环中所填充的5CB液晶指向矢的旋转角从0°到90°改变,二维环型光子晶体一直出现完全带隙,并且完全带隙随着液晶指向矢的旋转角的变化可以实现动态可调.分析完全带隙可调范围与二维液晶环型光子晶体的结构参数(液晶环内/外径、基底材料的折射率、液晶正常/反常折射率、内介质柱折射率)的变化关系.     

Real-time filter based on the quasi-accurate detection of gross errors

Because of the sensitivity of the Kalman framework to gross errors, proper techniques for detection of gross errors are necessary. By integrating the selection of quasi-accurate observations and the Kalman framework, a new filter called the quasi-accurate filter (QUAF) is developed. The expansibility and implementation scheme of the new algorithm are then discussed in detail, and the reliability matrix for the Kalman filter is proposed to analyze the reliability of the filters with different detection technologies. Finally, the experimental results from a real world case study are used to validate the conclusions. The QUAF carries out the preliminary selection of the quasi-accurate observations (QAOs) using the innovation of the Kalman filter, and use the check QAOs to determine reasonable observations. This causes the QUAF to handle more easily and possess wider expansibility. QUAF can be reformulated to the special cases of several common detection methods, such as the innovation method, robust estimation and quasi-accurate detection (QUAD). Since only reasonable observations are used, the QUAF has better detection accuracy and stronger avoidance of gross errors than the innovation method and robust estimation. Meanwhile, compared with QUAD methods, QUAF introduces the state-predicted model, requiring fewer quasi-accurate observations and making it more suitable for systems with complicated observation structures or sparse observations.     

Spatial discretization error in an artificial benchmark model of oblique laser incidence by finite volume approximation for radiative heat transfer

The spatial discretization error in a finite volume method approximation for radiative heat transfer is investigated. An artificial benchmark model for oblique laser incidence on a two-dimensional rectangle containing a semi-transparent medium is proposed, in addition to using reference data from the Monte Carlo method. Within the framework of the current model, it is shown that numerical scattering in the finite volume method is affected by the spatial grid values and the different spatial discretization schemes to a large degree. Numerical scattering also varies with the degree of absorption coefficient deviation. Numerical scattering is distributed in a symmetrical profile along the laser incidence direction, and all of the schemes show symmetrical cross-scattering.     

二阶双曲方程新非协调混合元格式分析

将非协调旋转1rot元应用到二阶双曲方程,建立了一个新的混合元格式.直接利用单元插值的性质,平均值及导数转移技巧,在正方形网格上,分别得到了原始变量及通量的H1-模及L2-模最优误差估计.     

定积分求解数列极限

定积分是数学的重要概念,在其他学科和各种领域应用广泛,在数学上的应用正向思维比较多,文章从逆向思维的角度,给出了利用定积分求解两种数列的极限的方法.     

聚集数据线性模型一种有偏估计

文章对病态的聚集数据模型,提出了新的有偏估计,其中对模型中的参数要求大于零。讨论了这种新的有偏估计的优良性,证明了此估计改进了岭估计(均方误差意义下),推广了已有的结果。     

基于USB的圆度误差测量系统设计

设计了一种基于USB的圆度误差测量系统．该系统以MSP430F149单片机作为下位机,由单片机自带的12位A／D模块采集传感器数据,通过USB接口芯片PDIUSBD12将数据传给上位机．上位机以LabVIEW为软件开发平台,利用LabVIEW强大的数据处理能力对采集的数据进行实时处理、分析和显示,实现了圆度误差的自动测量．与同类产品相比,该系统具有硬件电路简单、成本低、速度快等优点．     

指数宽带模型的数学回归及其应用

气体辐射特性参数的确定是求解辐射传热问题的关键,指数宽带模型能够较为准确地对其进行求解,但该方法计算过程复杂,求解速度慢,不适于在线应用.针对加热炉内的烟气成分CO2和H2O,以炉子生产时烟气和炉子内表面的温度为计算范围,通过对指数宽带模型求解结果的分析,将其在各谱带的参数回归成随温度或压力变化的函数表达式,简化了宽带模型中复杂参数的求解过程.在保证精度的前提下,提高了指数宽带模型的计算速度.     

GPS测量误差来源与处理方法探讨

GPS技术是重要的测量技术之一,被广泛应用在各类测量活动中。针对GPS测量中的误差来源,从信号源、信号传播与信号接收3个方面进行了分析,给出了处理这些误差的方法,包括模型改正法、求差法和回避法。