相离两圆中的矩形

从相离两圆的圆心分别向另一圆作两条切线，切线与圆的四个交点必为一矩形的四顶点．     

矩形毛细微槽中三角形区域接触线特性的研究

利用CCD和宽视场体视显微镜相结合的技术,拍摄了矩形毛细微槽内液体工质在三角形区域的润湿图像,并进行了图像处理,研究结果表明:随着热流密度的增加,三角形区域内的三相接触线向微槽底角收缩,导致三相接触线的长度减小,液膜厚度减小;随着微槽深度的增加,三角形区域的接触线长度减小;随着微槽宽度和倾斜角度的增加,三角形区域内的接触线长度增加,液膜厚度增加.     

让学生在问题设计中发现——引导学生“再创造”《矩形判定》的教学研究

1 引言著名的数学教育权威弗赖登塔尔认为,数学教学方式的核心是学生的"再创造".如何通过数学教学培养学生这种问题意识?训练学生这种问题意识?一直是笔者多年的追求.应无锡英桥国际学校之邀,笔者上了《矩形判定》的新授课,本文结合课堂实录与点评,汇报自己的教学思想,以求更多老师帮助.     

一道习题的深入探究

高中数学新人教(A版)选修2-1习题2.2(B)组第4题:如图,矩形ABCD中,|AB|=8,|BC|=6.E,F,G,H分别是矩形四条边的中     

电喷雾/光电离双源型小型离子阱质谱仪的研制

构建了一套电喷雾/紫外灯双电离源离子阱质谱仪系统,用于气体和液体样品的快速检测.仪器采用非连续大气压进样技术,通过夹管阀装置来同时完成电喷雾离子和中性气态样品的采集和传输.所配备的两种电离源适合不同的分析对象,在应用上具有一定的互补性,其中电喷雾源用于溶液中极性化合物的电离,而紫外电离源主要用于分析气态有机物.本研究选择了苯甲醚、甲苯、2,4-二甲基苯胺、精氨酸、利血平和阿斯巴甜等不同类型的样品,测试了仪器在使用不同电离模式下的工作性能.结果表明,电喷雾源和紫外光电离源可用于不同类型样品的电离,在分析2,4-二甲基苯胺时还能分别生成不同类型的分子离子.两种电离源在工作时互不干扰,既能单独使用,也能同时开启,可根据检测需求随意切换工作模式,获得更全面的样品成分信息.双离子源设计是扩展小型质谱仪应用范围的一种有效途径,这种方案不会明显增加仪器的体积,却能提供更多样化的分析功能,满足对不同类型样品的检测需求.     

矩形多环芳烃的合成

本文用3,4-二苯基-2,5-二(3,5-二溴苯基)环戊二烯酮(4a)与二苯乙炔(5a)通过Diels-Alder环加成反应得到1,2,4,5-四苯基-3,6-二(3,5-二溴苯基)苯(6a)。化合物6a通过经典的Suzuki偶联反应得到1,2,4,5-四苯基-3,6-二(3,5-二(4-十二烷基噻吩))苯基苯(8a),再利用Fe Cl3作为氧化剂发生Scholl氧化脱氢关环反应,得到目标化合物1a。采用类似合成方法,得到目标化合物1b。化合物的结构均通过1H NMR和MALDI-TOF MS表征,并对其光谱特征、热性能及电学性能进行了初步研究。     

Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints北大核心CSCD

Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

类比学习路径 重视探究过程——以“矩形的判定”再设计为例

基于对《课标(2022版)》的研读,本文中对“5.1.2矩形的判定”进行再设计.类比平行四边形研究路径,通过对矩形判定定理“引入—发现—猜想—验证—表述—应用”的探究,体现定理学习的一般过程,提高学生思维品质.     

矩形微通道中气–非牛顿流体两相流实验研究

本文通过实验研究了空气与非牛顿流体在小尺寸矩形微通道中的两相流动特性,给出了在不同气液两相流速下的流型图。同时比较了气液两相流速,液相黏度,表面张力,微通道尺寸对各流型分布区域以及Taylor气泡/液柱长度的影响。发现气液两相流流速变化对流型区域的影响极为明显,而黏性力和表面张力只是在局部范围改变了流型分布。Taylor气泡长度随气液两相流速比增大而增大,随液相黏度及表面张力增大而减小。液柱长度随液相黏度增大而增大,随两相流速比及表面张力增大而减小。最后,我们给出了基于无量纲数JG/JL,Re和Ca的Taylor气泡/液柱长度预测公式,公式预测结果与实验结果基本一致。