用整体思维处理高考题

用整体思维处理高考题３５２２００福建古田教师进修学校魏铮整体思维是控制论、信息论、系统论中整体原理在数学解题中的反映，是一个重要的数学思维方法．它在数学解题中表现为不拘泥于问题的各个组成部分，将要解决的问题看作一个整体，通过研究问题的整体形式和结构特...     

High-accuracy self-mixing interferometer based on multiple reflections using a simple external reflecting mirror

A self-mixing interferometer (SMI) with resolution twenty times higher than that of a conventional interferometer is developed by multiple reflections. Only by employing a simple external reflecting mirror, the multiple-pass optical configuration can be constructed. The advantage of the configuration is simple and easy to make the light re-injected back into the laser cavity. Theoretical analysis shows that the resolution of measurement is scalable by adjusting the number of reflections. The experiment shows that the proposed method has the optical resolution of approximate λ/40. The influence of displacement sensitivity gain (G) is further analyzed and discussed in practical experiments.     

透视教例 优化学生解题思维品质

本文旨在对教材一典型例题的全方位透视,探讨寓优化学生思维品质的训练和培养于日常数学教学活动之中的方法。 1.全方位扫描,培养思维的广阔性 思维的广阔性是指能全面完整地、多角度地考虑问题。教师应该深入钻研、透彻分析教材,正确完整理解数学知识的精髓,在主导知识传播过程中,全面地、多角度和立体式地训练和培养学生思维的广阔性。     

巧列繁分式方程解题

李政道教授一九七九年春访问中国科技大学和科大少年班与同学见面时,提出了: 海滩上有一堆苹果,这是五个猴子的财产,它们要平均分配,第一个猴子来了,它左等右等,别的猴子都不来,它便把苹果分成五堆,每堆一样多,还剩下一个,它把剩下的一个扔到海里,自己拿走了五堆中的一堆,第二个猴子来了,它又把苹果分成五堆,又多了一个,它又扔掉一个,拿一堆走了。以后每个猴子来了,都是如此办理,问原来至少有多少苹果?最后至少有多少苹果? 问题提出后《数学通报》等数学杂志提出了多种解法,有的运用线性方程组的通解理论,有的通过计算迭代函数,这些方法都要     

正多边形的复数定理

让我们先证明一个定理:如果在复平面上,A、B、C三点对应的复数分别为:Z_1、Z_2、Z_3,且△ABC为正三角形,则wz_1 w~2z_2 z_3=0 (1)     

Non-invasive human extremely weak pulse wave measurement based on a high-precision laser self-mixing interferometer

In this paper, a technique based on laser self-mixing effect for acquiring pulse wave profile is proposed and demonstrated. For the characteristics of extremely weak vibration in human pulse waves, a method of multiple reflections with external cavity is designed to improve the measurement accuracy to λ/4. Based on the fringe counting algorithm, one period of pulse wave is successfully reconstructed. The measurement results show that the root mean square error (RMSE) of the reconstructed pulse wave is 0.912 μm at sampling rate of 8 kHz. Besides, the correlation coefficients and heart beats of this method and the traditional photoplethysmography (PPG) measurement are analyzed.