另类“数形结合”帮助学生理解几何证明*--由平行四边形判定教学引发的一点思考

恩格斯曾说过：“数学是研究现实世界中量的关系与空间形式的科学。”数形结合就是根据数学问题的条件和结论之间的内在联系，既分析其代数意义，又揭示其几何直观，使数量的精确刻画与空间形式的直观形象巧妙、和谐地结合在一起，充分利用这种结合，寻找解题思路，使问题化难为易、化繁为简，从而得到解决。其实按笔者的理解，初中的几何证明就是一个数形结合的好例子。它让学生用文字与符号，对图形进行分析与解释。让学生在思考图形的来龙与去脉的过程中，逐步学会逻辑思考，慢慢学会理性思维。但也因此让许多学生感到十分头痛，易产生畏难情绪。     

左Clifford半群的特征与结构

作为Clifford半群的推广,本文定义了左Clifford半群,给出了它的许多特征,建立了它的半格分解结构和ξ直积结构。还讨论了两类特殊情形。     

一类阿基米德半群的构造及其同余格

本文引入同底的π-左、右零半群的夹群积并用来刻划带本原幂等元的阿基米德半群的构造.文中讨论了有限阶阿基米德半群的同余格,并证明了当有限阶阿基米德半群的正则R,L类的个数不超过5时,它的同余格是半模格.     

七-O-乙酰基-β-乳糖异硫氰酸酯的合成、表征及电化学研究

本文合成了并培养出了七-O-乙酰基—β—乳糖异硫氰酸酯的单晶，用X射线衍射分析了其晶体结构。结果表明，晶体为正交晶系，P2₁2₁2₁空间群，a＝1．23282(7)，b＝1．80012(10)，c＝1.85230(10) nm，α＝β＝γ＝90°，V＝4．1107(4) nm³，Z＝4。电化学实验观测到单链DNA和双链DNA对该化合物的峰电流均有明显降低作用，表明化合物与DNA发生了静电作用。     

共轭高分子的研究——Ⅶ.脂肪腈类的聚合

<正> 聚腈作为新的一类共轭高分子而引起注意。本文在前报的基础上进一步选择了一系列脂肪腈(乙腈、丙腈、戊腈、庚腈和苯乙腈),系统地研究它们在络合能力较强的付氏试剂(BF_3和TiCl_4等)作用下的聚合反应与机理,同时测定了各聚腈的物理性能。 1.腈的络合聚合 腈类与付氏试剂可形成定组成的络合物结晶:     

Impact Responses of Prismatic Lithium-Ion Battery Based on the Membrane Factor Method北大核心CSCD

Aimed at the internal short circuit problem due to large deformation of the prismatic lithium-ion battery cell under impact loadings, a simplified battery model was first established. Then the motion equations of velocity and displacement based on the membrane factor method were proposed. With the effects of the face-sheet thickness and the densification region on the normalized final deflection, impact response characteristics of prismatic battery cells were investigated in detail. The results show that, the improved motion equations involving the membrane factor can reflect the dynamic response mechanisms of the prismatic battery cell under impact loadings, and the large deflection under high-speed impact can be predicted. With the increase of the face-sheet thickness, the deflection of the battery cell’s lower part decreases obviously. However, the densification region expands with the face-sheet thickness. The deflection and the densification region of the cell’s lower part both increase with the inner core density of the battery. This proposed impact model provides a theoretical guidance for the multi-functional integrated dynamic design of prismatic battery cells. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

14N遥测核四极共振中的偏离共振效应

本文对遥测NQR谱中的偏离共振效应作了较详细地研究,发现¹⁴N谱线的强度随偏离共振效应而变化。当偏离共振强度与射频场强度接近时,测得的谱线强度最大。该效应可用来增强¹⁴N遥测NQR谱仪的灵敏度。上述实验现象在理论上采用脉冲的激发带宽方法作了解释和讨论。     

烷氧钇及含双键的烷氧钇单体的合成及其结构表征

合成了十种含双键的烷氧钇单体Ｙ（ＯＲ）３－ｎ（ＣＯＯＣＨ＝ＣＨＣＯＯＲ）ｎ，（ｎ－１或２，Ｒ为烷基），并用钇含量分析、红外光谱、核磁共振谱对其结构进行了表征。     

咪唑-金属配合物的合成、性质及其与DNA的作用机理

Three hexakis（imidazole）metallo complexes of Co, Cd and Ni were synthesized and spectroscopically characterized. The crystal and molecular structures have been determined by X-ray crystallography analysis. The metal ions have an octahedral geometry with the MN6 chromophore. The electrochemical experimental results indicate that both [Co（Im）6]C12·2HCl·2H2O （1） and [Ni（Im）6]C12·4H2O （3） [Im=imidazole] could interact with DNA mainly by intercalation.     

四氮大环-金属配合物与DNA作用的电化学及谱学研究

Mononuclear copper（Ⅱ）, nickel（Ⅱ） and cobalt（Ⅲ） tetracoordinate macrocyclic complexes were synthesized and spectroscopically characterized. The crystal structure of the three compounds were determined by X-ray crystallography. The electrochemical experimental results indicate that the three complexes could interact with DNA mainly by electrostatic interaction. The interaction of tetracoordinate macrocyclic cobalt（Ⅲ） complex with DNA was studied by cyclic voltammetry and UV-vis spectroscopy. The experimental results reveal that tetracoordinate macrocyc- lic cobalt（Ⅲ） complex could interact with DNA by electrostatic interaction to form a 1 ： 1 DNA association complex with a binding constant of 7.50 ×10^3 L·mol^-1.