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关键词： athletics   baton exchange   running   sprinting  

摘要： Using mathematical analysis, we examined the three baton exchanges that occur during a 4x100 m relay. Identical representative 100 m running performances were assumed for each of four elite male athletes, and the calculations were made for optimal or near-optimal positions of the baton exchanges and starting positions of the athletes running the second, third and fourth legs as determined by Ward-Smith and Radford (2002). In this paper, we focus on the calculation of the checkmark position and demonstrate the complexity of the baton exchange process. The results of the mathematical analysis show that, for optimal performance, the checkmark should be located differently for each of the three exchanges in a single race, and is further affected by lane draw and free distance (the distance between the runners at the baton exchange). For a representative free distance of 1 m at each exchange, the checkmark distance ranges from a minimum of 11.04 m at the third exchange in Lane 1 to 12.20 m for the first exchange in Lane 8. Failure by teams and their coaches to consider adequately the complexities of the baton exchanges may help explain why 25.5% of teams in recent World Championships were disqualified or did not finish.

关键词： 数学分析   专题研究   电视大学   教材  

ISBN: (纸本)7304024143

摘要： 教育部人才培养模式改革和开放教育试点教材 数学与应用数学专业系列教材:本书共分六章：第一章为集合与关系，第二章为数集，第三章函数，第四章为指数函数与对数函数，第五章是三角函数，第六章为极值问题。

ISBN: (纸本)7308014711

ISBN: (纸本)7040118882

关键词： 行车颠簸问题   数学分析   数学   解题   教学   代数   初中  

关键词： Fast nitrogen-ions   X-ray-diffraction   Crystals  

摘要： A reciprocal space map recorded by means of a high-resolution diffractometer is a function of two angular variables: omega and 2theta defined as angular position of the studied crystal and position of an analyser, respectively. For comparative investigations of different samples the inter-planar spacing distribution function and the lattice reflecting plane orientation distribution function are more useful. In this paper we present the integral equations, which allow one to obtain these functions through the integration of the reciprocal space map matrix. An example of the mathematical analysis of the reciprocal space map for GaAs single crystal recorded by means of a Philips MRD high-resolution diffractometer is described and well-defined analytical formulae for the apparatus functions are given.

关键词： 固定床吸附   活性炭   烟气脱硫   穿透特性   数学分析  

摘要： 该文针对固定床活性炭脱硫中面临的问题,通过试验研究,分析影响固定床活性炭脱硫的穿透特性的因素,得到了几个基本参数,并采用数值积分的方法对所建模型进行了数值分析.研究结果表明,对于不同粒径的活性炭,穿透点随着粒径的增大而前移,穿透时间在缩短.而随着入口SO<,2>浓度的增大,穿透时间在缩短.通过对处于平衡态前后的活性炭进行穿透试验,可以看出,平衡态后的活性炭穿透曲线比平衡态前的穿透曲线左移,穿移时间缩短,穿透点前移.通过对几种活性炭的τ-L曲线的测定,可以看出,随着SO<,2>浓度的增大,每种活性炭的吸附区长度都在迅速增大,吸附层保护作用系数在减小,保护作用时间在缩短.而随着活性炭粒径的增大,吸附区长度在增大,吸附层保护作用时间在缩短.采用直接积分求解法以代替原有的数值积分求解法,对穿透曲线进行了预测.结果表明,此模型在预测穿透点以及吸附容量方面和试验能够较好的吻合,可以用于固定床吸附低浓度二氧化硫的有关参数的预测及工业装置放大的模拟.

关键词： 《数学分析》教学   数学阅读   示范教学   高等师范教育   数学教学  

摘要： 数学阅读示范为学生阅读数学书树立了榜样,改变了学生对数学阅读的看法,改变了学生阅读数学书的习惯,提高学生阅读数学书的自觉性。

关键词： 物理教学   情景教学   数学定理   能力培养   情景设置   数学分析   创新意识  

摘要： 将物理情景转化为数学情景,然后运用数学手段分析、处理物理问题的能力是物理教学中加强能力培养的一个重要方面.而巧设物理情景,运用物理原理来解决数学问题则可看作是培养创新能力、落实创新教育的一个重要侧面.因此,习惯了借助数学手段分析、处理物理问题的我们,若能尝试一下通过对物理情景的巧设,然后运用物理原理来证明有关数学定理将会收到意想不到的效果.笔者在此特举例,以起抛砖引玉之功效,不足之处还请同行指正.

关键词： 数学分析   金属小球   光滑圆轨道   平抛运动   轨道脱离   高中   物理