分类讨论的数学思想及其应用（4）

第四讲：分类讨论的运用（一）从前面三讲中我们已经知道,解分类讨论题的主要过程是进行逻辑划分和对每一类做出讨论、证明、求解等等．高考不仅是数学知识的考查,也是数学思想方法的考查．高考的“能力立意”,主要是通过在数学思想的指导下,如何运用数学方法解决问题来体现的．     

高中生逻辑推理能力的调查研究——以南京市为例北大核心

1问题的提出 推理是数学的基本思维方式,也是人们学习和生活中经常使用的思维方式,从数学本身看,数学推理反映的是一种基本的数学思想,也是一种主要的数学方法,它与数学证明紧密关联,共同构成了数学最重要的基础．     

在数学教育中进行适时的科技渗透

在高中"球"的教学中,将"神舟六号"载人飞船成功发射这一重大科技成果作为载体,可以使学生亲身感受到数学的巨大魅力,数学能帮我们科学思考问题,并对各种媒体提供的数据用数学方法加以检验.     

共价键中结合力的本质及其强度的定量表达方法: 键强参数的概念

建立A-B键中某价电子的键强参数的概念, 表达价分子轨道i上一人电子对A-B键中化学结合力的贡献。从理论上说明它是i-电子云对A及B核的"拉力"以及对其它电子的"推力"的"净效应"大小, 就CO, N2, O2说明其所反映的"成键性质"与UPS的实验数据相一致。就几个均匀环状化合物证明其有很好的"加和性"。多中心键的F1与其中"双中心"键的f1之和相等。其所反映的"成键"性质MO的对称性及电荷密度分布图的定性结论完全一致。表达式所反映的键强度与键长及"键电荷"的大小顺序相适应。     

Nonfactorizable B→xcoK Decay and QCD Factorization

We study the unexpectedly large rate for the factorization-forbidden decay B→χ_c0K within the QCD factorization approach. We use a non-zero gluon mass to regularize the infrared divergences in vertex corrections. The end-point singularities arising from spectator corrections are regularized and carefully estimated by the off-shellness of quarks. We find that the contributions arising from the vertex and leading-twist spectator corrections are numerically small, and the twist-3 spectator contribution with chiral enhancement and linear end-point singularity becomes dominant. With reasonable choices for the parameters, the branching ratio for B→χ_c0K decay is estimated to be in the range (2～4)×10^-4, which is compatible with the Belle and BaBar data.     

《应用数学和力学》来稿简则

1.我刊主要刊登有关力学、力学中的数学方法和与近代力学密切相关的应用数学的创造性学术论文。我刊以中、英文两种版本公开发行,惠稿请提供内容相同的中、英文稿电子文档。稿件力求简短,一般在3000～5000字左右,以不超过8000字为宜。     

Journal of Mathematical Research and Exposition Guide for Authors

Journal overview： Journal of Mathematical Research and Exposition （JMRE） was created in 1981 to promote mathematical research and to report and review theoretical and applied results in mathematics. This journal is devoted to original research articles of the highest quality in all areas of pure and applied mathematics. Short communications, survey or review articles, and articles on mathematical methodology and mathematical philosophy are welcome. In addition,     

一道中考模拟压轴题的解法探究与思考

在南京市组织的一次初三数学中考模拟练习中,一道压轴题让很多学生望而却步、思路受阻,得分率很低.笔者悉心研究发现,对于此题,只需抓住题目条件特征、图形特征和结论特征中的一个,运用基本数学模型和基本数学方法,即可自然求解.下面将解法探究呈现给大家,以飨读者.一、题目如图1,已知直线l与线段AB平行,试只用直尺作出AB的中点.1.初步探索如图2,在直线l的上方取一个点E,连接EA、EB,分别与l交于点M、N,连接MB、NA,交于点D,再连接ED并延长交AB于点C,则C就是线段AB的中点.     

A SEMI－ANALYTICAL AND SEMI－NUMERICAL METHOD FOR SOLVING 2－D SOUND－STRUCTURE INTERACTION PROBLEMS

Based on the transfer matrix method and the virtual source simulation technique,this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound-structure interaction problems under a harmonic excitation. Within any integration segment,as long as its length is small enough, along the circumferential curvilinear coordinate, the nonhomogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper. For the exterior fluid domain, the multi-circular virtual source simulation technique is adopted. The source density distributed on each virtual circular curve may be ex-panded as the Fourier‘‘s series. Combining with the inverse fast Fourier transformation, a higher accuracy and efficiency method for solving 2-D exterior Helmholtz‘s problems is presented in this paper. In the aspect of solution to the coupling equations, the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper. According to the superposition principle and compatibility conditions at the interface between the elastic ring and fluid, the algebraic equation of system can be directly constructed by using the least square approximation. Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented. Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.