关于数学建模课程的一些思考

数学建模课程的教学目标是培养学生应用数学解决实际问题的能力.根据多年的教学实践经验,本文探讨如何在教学过程中注重数学思想方法的传授和能力的培养.对目前教学过程中存在的一些问题进行了剖析.介绍了我们在课程的课外延拓方面所做的一些工作.     

基于近似解析法的超导储能磁体设计

降低超导储能磁体的研制成本一直是控制超导磁储能系统(Superconducting Magnetic Energy Storage, SMES)总成本的重要手段之一.本文考虑在一定磁体结构参数范围内,磁体产生的最大磁场值可以采用级数进行表示,磁体的电感值可以采用线性函数表示,给出了超导储能磁体磁场能量的近似解析表达式,提出了一种基于近似解析法的超导储能磁体设计方法.该方法以储能磁体的线材用量最小作为设计目标,在给定超导线材参数和临界电流特性曲线,以及磁体储能总量要求的情况下,依据此方法可快速的得到成本最优时所对应的磁体结构参数.将近似解析法优化和采用传统的有限元软件Ansys仿真优化进行对比分析,结果表明采用近似解析法进行磁体优化更加方便快捷,节省了大量计算时间.     

一流课程背景下大学物理课堂演示实验的实践及效果分析

近年来教育部提出实施一流课程建设.大学物理是理工科专业重要的基础课,在理论课堂上引入演示实验来辅以教学,对提高学生对物理的兴趣和重视程度及对人才培养质量的提升尤为重要.本文对大学物理课程旋转矢量法知识点教学中开展演示实验,通过讲解知识点之前、演示实验之后以及经过一周后三次测试数据分析,考查演示实验对学生学习成效的效果,...     

便携式FTIR的机动车尾气检测方法

随着汽车排放标准的提高,相关VOC标准从总烃检测变为非甲烷碳氢化合物(NMHC)检测;随着含氧燃料的增加,增加了非甲烷有机气体(NMOG)测量.针对国内汽车尾气分析仪分析组分单一、精度有限、VOCs检测过程复杂等问题,提出了基于便携式FTIR的机动车尾气检测方法,基于立体角镜优化FTIR光学系统结构,提高动镜扫描速度,...     

二维剪切波面重建的有限元模型

提出了解析二维剪切波面的有限元方法，建立了二维剪切波面重建的有限元模型。计算模拟结果表明，有限元法解析二维剪切波面精度高，对剪切波面具有平均作用，对测量误差不敏感，可适用于实时测量。     

一个数学问题推广结论的纠正

《数学通报》数学问题1845和1990是同一道题:已知a＞0,b＞0,√3/a+1/b=2,求a+b-√a2+b2的最大值. 文[1]对此题有如下两个猜测推广: 推广1若a＞0,b＞0,m/a十n/b=1(其中m,n为正常数),则a+b-√a2+b2的最大值为2m+2n-2√2mn.     

Experimental study on laser cleaning of paint layer on white marble surface北大核心CSCD

In order to effectively remove the surface paint of the cultural relic of white marble, the area extrapolation method and laser-induced plasma spectroscopy (LIPS) method were used to obtain the ablation threshold power of the gold, silver paint layer and white marble surface. On the basis of this, the optimal laser power for removing paint without damaging the white marble substrate was determined. The image processing method was used to study the cleaning degree and variation trend of cleaning rate of the gold and silver paint on the surface of 10 mm×10 mm white marble by laser cleaning, and the optimal laser spot overlap rate and the optimal cleaning times were obtained. Finally, the image processing method was used to evaluate the cleaning effect of laser cleaning of paint layer on the white marble surface. More than 93% of the cleaning degree shows that the synergistic use of the area extrapolation method, LIPS method and image processing method can effectively improve the laser cleaning efficiency of the paint layer on white marble surface. Copyright ©2022 Journal of Applied Optics. All rights reserved.     

Geometric quantities of lower doubly excited bound states of helium

Expectation values of single electron and interelectronic geometric quantities such as $\langle r\rangle$, $\langle r_{12}\rangle$, $\langle r_<\rangle$, $\langle r_>\rangle$, $\langle \cos\theta_{12}\rangle$ and $\langle \theta_{12}\rangle$ are calculated for doubly excited $2{\rm p}n{\rm p}\,{}^1P^{\,\rm e}\,(3\leq n\leq5),\, 2{\rm p}n{\rm p}\,{}^3\!P^{\,\rm e}\,(2\leq n\leq5)$ and $2{\rm p}n{\rm d}\,{}^{1,3}D^{\,\rm o}\,(3\leq n\leq5)$ states of helium using Hylleraas-$B$-spline basis set. The energy levels converge to at least 10 significant digits in our calculations. The extrapolated values of geometric quantities except for $\langle \theta_{12}\rangle$ reach 10 significant digits as well; $\langle \theta_{12}\rangle$ reaches at least 7 significant digits using a multipole expansion approach. Our results provide a precise reference for future research.     

a-Si:H掺杂机理的研究

本文利用CNDO/2量子化学理论方法,对P和B原子在四面体配位的Si₄₆和Sl₄₆H₆₀H₄^*原子集团中置换Si原子前后的原子集团能量和能态分布变化进行了计算.计算结果表明:1)在Si₄₆H₆₀H₄^*原子集团中用P(或B)置换引Si原子后在能隙中明显地出现施主(或受主)态子带,同样在Si_{46相似文献}   

New characterizations of Hajlasz-Sobolev spaces on metric spaces

This paper introduces the fractional Sobolev spaces on spaces of homogeneous type,includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels.The author establishes varions chaaracterizations of(sharp)maximal functions for these spaces.Asapplications,the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces.Moreover;some embedding theorems are also given.