南部侗歌旋律“依字行腔”特征及其原理之数学演算

文章首先通过对侗族南部方言区民歌的五步骤分析,总结了"依字行腔"现象在侗族民歌音乐创作中存在的事实。其次采用五进制和七进制的数学转化方法和简单计算,解释了"依字行腔"这种语言声调向音乐音高旋律转化现象的原理和过程。

Calculus of the Railway Vertical Stiffness Depending on the Base Plate Stiffness and the Ballast for High Speed Railways

The study aims to determine a mathematical formula that correlates the vertical stiffness of the principal elements of a high speed railway. To do this, beginning on the traditional formulations, a new mathematical model has been proposed, and has been verified and confirmed with the real information of high speed railways. Finally, there has been obtained a simple expression that correlates simply the vertical stiffness of the railway with the vertical stiffness of the elements that compound it, essentially with the base plate and the ballast system set. On the other hand, also the accuracy of the model has been verified to select the stiffness of the base plate and the ballast system depending on one of this stiffness and the total vertical stiffness that it is wanted. With this simplified formula, it is possible to optimize the vertical stiffness of the railway to obtain the best behavior in each zone and to reduce the final cost of the use of the via, taking in consideration the energy needed to move the trains, the maintenance cost, the useful life, etc.. The process to optimize the railway stiffness in each point depends on the vertical stiffness of the ballast and the sub-ballast, and it is possible to use different plate bases with different stiffness to obtain the optimal stiffness that has been previously obtained with a cost and maintenance analysis.

后期维特根斯坦论逻辑和数学的基础

国外维特根斯坦研究中的一种流行看法,即认为维特根斯坦不懂数学,而通过大量的论证和分析证明,维特根斯坦并非真的不懂数学,相反,他对数学基础和逻辑推理的看法,充分反映了他对这些问题的深刻理解。同时,维特根斯坦对逻辑和数学基础问题的评论,体现了他后期哲学的基础精神。