浅谈数学中的变形技巧

变形技巧在数学解题中是很常用的方法,数学解题中,为了完成论证,求值、化简等的任务,需要对一些式子进行恒等变形。一般情况下,一个式子往往有多种变形形式,因题而异,技巧性非常强。本文主要介绍了在初高中数学中的三角函数、因式分解、不等式、一元二次方程等的变形应用。掌握好并灵活运用好变形技巧,可以化复杂为简单,提高解题效率。     

求KP方程行波解的形变方法

本文找到了形式上完全不同的非线性KdV方程和KP方程行波解之间的形变关系,从已知的KdV方程的解得到了KP方程的许多新解。     

The Influence of Tian Gan Deflection on the Flatness of Hanging Scrolls in Chinese Painting and Calligraphy

ABSTRACT

The forms of traditional Chinese painting and calligraphy are varied, including hanging scrolls, horizontal scrolls, screens, hand scrolls, and albums. Hanging scrolls are hung on the wall for display, but curling edges often appear on both sides of the hanging scroll. Various factors influence the deformation of paintings and calligraphy, such as temperature and relative humidity and the susceptibility of materials in scrolls as well as mounting techniques. The influences of structural components, such as tian gan (hanging rod), hanging rope, and di gan (lower rod) have received little attention. This paper focuses on the influences of tian gan deflection on the deformation of hanging scrolls, with the help of DIC (digital image correlation) visualization. Deflections of tian gan in two types of hanging methods were compared with a theoretical study. It was suggested that the influence of axial force was of great importance on the increase in deflection and bending moment. To reduce the bending of tian gan as much as possible, the vertical hanging method with appropriate position for the hanging rope should be chosen for mounting hanging scrolls.     

拉伸法测杨氏模量中的横梁形变对实验的影响

拉伸法测定金属的杨氏模量实验中,一般采用光杠杆测量出细丝因受拉力而产生的微小伸长量,测出的金属丝微小形变量是否精准决定了这个实验精确度。光杠杆测量出细丝因受拉力而产生的微小伸长量理应该包括了横梁弯曲的形变量。为减小横梁形变带来的影响,提高拉伸法测杨氏模量的实验精度,可从对金属丝的形变量进行修正和改变横梁结构两方面着手。     

非连续变形分析中方程组的并行化求解方法

非连续变形分析是针对非连续介质的数值计算方法。该方法存在计算效率较低的问题,而方程组求解是瓶颈。研究非连续变形分析在不同的计算条件下,选择不同的方程组求解方法可获得的计算效率。基于OpenMP与CUDA分别并行实现Jacobi迭代法与Jacobi预处理共轭梯度法,分析问题规模、计算时步长、块体接触关系对方程组求解效率的影响。通过算例测试,获得不同条件下选择方程组求解方法的经验公式,可有效指导非连续变形分析的并行方案设计。     

求非线性薛定谔方程的行波解的一种新途径

利用形变映射法,建立NLS方程与Klein-Gordon（NKG）非线性方程的一类特殊类型解的代数变换关系,根据NKG方程的已知解,获得NLS方程系统丰富的显式精确行波解,包括孤波解,周期波解,雅可比椭圆函数解.     

影响汽车板深冲性能的因素分析

以取向硅钢的径向(与轧向分别成0°、25°、45°、55°、70°和90°)拉伸变形行为为案例,探讨影响汽车板深冲性能的因素。结果表明,材料的滑移系和强度是影响其延伸率和深冲性能的两个重要因素。由于具有强烈的γ-纤维织构的汽车板法向强度高、径向强度低,并且各向异性小,延展性好,因此其深冲性能极好。利用X-射线织构分析技术可以较好地评估其深冲性能。     

软土地区路基扩建工程变形监测分析

以某湖区公路路基拓宽工程为依托,建立沉降、位移监测体系,通过长时间的数据监测结果,分析了新老路基不协调变形的发展规律,为类似湖区公路路基拓宽工程的施工提供指导。     

基于特征缺失修复的人脸三维运动形变估计算法

人脸由于其非刚性明显,受到运动背景变化、形变程度复杂、特征丢失等因素的影响,使得在进行三维动态人脸形变估计时,面临着估计不准,误差较大的问题。为了解决这些问题,提出一种基于特征缺失修复的人脸三维运动形变估计算法,将非刚体人脸运动的形变估计过程中,运用特征补偿方法,补偿由于噪声、形变程度复杂带来的特征丢失缺陷,运用较多的人脸形变特征进行形变分析,准确计算人脸的形变程度。实验结果表明,这种方法得到的解误差较小,效果明显。     

Estimation of the energy loss at the blades in rowing: Common assumptions revisited

Abstract

In rowing, power is inevitably lost as kinetic energy is imparted to the water during push-off with the blades. Power loss is estimated from reconstructed blade kinetics and kinematics. Traditionally, it is assumed that the oar is completely rigid and that force acts strictly perpendicular to the blade. The aim of the present study was to evaluate how reconstructed blade kinematics, kinetics, and average power loss are affected by these assumptions. A calibration experiment with instrumented oars and oarlocks was performed to establish relations between measured signals and oar deformation and blade force. Next, an on-water experiment was performed with a single female world-class rower rowing at constant racing pace in an instrumented scull. Blade kinematics, kinetics, and power loss under different assumptions (rigid versus deformable oars; absence or presence of a blade force component parallel to the oar) were reconstructed. Estimated power losses at the blades are 18% higher when parallel blade force is incorporated. Incorporating oar deformation affects reconstructed blade kinematics and instantaneous power loss, but has no effect on estimation of power losses at the blades. Assumptions on oar deformation and blade force direction have implications for the reconstructed blade kinetics and kinematics. Neglecting parallel blade forces leads to a substantial underestimation of power losses at the blades.