余弦定理的向量公式

式子｜a｜=√a·b之所以有用,原因在于它建立起长度与数量积运算间的关系．类似地,对于余弦定理,如图1,     

例谈平面向量数量积的求值问题

平面向量的数量积是向量中的一个重要的概念,它有物理背景和几何意义,有自己的运算律与坐标运算公式,能把代数与几何等内容巧妙地结合在一起．在近年的高考卷与模拟测试卷中,经常见到求平面向量数量的值或它的取值范围的问题．就这一类问题的解决思路与方法,本文结合一些例子,做一些梳理,以期举一反三,启迪思维．     

The Exact Traveling Wave Solutions to Two Integrable KdV6 Equations

The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that thes...     

SL(n,C)中可解子群结构及几类可积型Fuchsian系统(英文)

本文研究并给出一类SL(n,C)中的有限生成的可解子群结构定理.利用单值群的可解性与Fuchsian方程的可积性关系,给出几类可积型Fuchsian系统.     

动生电动势的几何意义

根据动生电动势中包含的矢量混合积,分析动生电动势的几何意义.在此基础上,对导体在磁场中运动产生的动生电动势用动生电动势的定义和求体积的方法进行求解,并从几何意义上对导体在磁场中运动时不产生动生电动势的情况进行说明.     

温度对水的离子积与溶液酸碱性的pH判据的影响

讨论了温度对水的离子积Kw和溶液酸碱性的pH判据的影响,分析了容易产生的模糊认识.Kw随温度升高显著增大,使溶液呈中性的pH(中性pH = pKw/2)在高温(>25 ℃)和低温区(<25 ℃)分别出现小于和大于7.0的情况.     

关于积图点可区别边染色的若干结论

如果图G的一个正常边染色满足任意两个不同点的关联边色集不同, 则称为点可区别边染色(VDEC), 其所用最少颜色数称为点可区别边色数. 利用构造法给出了积图点可区别边染色的一个结论, 得到了关于积图点可区别边色数的若干结果, 并且给出25个具体积图的点可区别边色数, 验证了它们满足点可区别边染色猜想(VDECC).     

A NOVEL THEORY OF EFFECTIVE MECHANICAL PROPERTIES OF CLOSED-CELL FOAM MATERIALS

In this paper a new theory of effective mechanical properties of foam materials is proposed. A cell volume distribution coefficient is introduced to modify the original Gibson-Ashby equations of effective mechanical properties of foam materials. The constants that influence the effective modulus are replaced by the coeff~cient. Based on the modified distribution coefficient, the yield stress is also recalculated. Using X-ray microtomography, the internal structures of dif- ferent samples of polypropylene-nanoclay foam are obtained. The cell volume distributions of these samples are derived from the experiment by image analysis and the fitting curves are plot- ted. The distribution coefficient is acquired using the parameters from the theoretical model of the distribution curves. The results of the improved theory are compared with the experimental values and show good fitting quality. It was found that the precision of the improved theory is high and the cell volume distribution has an impact on the effective mechanical properties that would lead to the optimization of the synthesis procedure.     

完全多部图与完全图Kronercker积的点参数研究

若G1和G2是两个图,G1和G2的Kronecker图定义为V (G1×G2)= V (G1) × V (G2 E(G1 × G2)= {(u1,v1)(u2,v2)。在本文中,我们计算了p-部完全图 m1,m2,...,mp 和完全图Kn 的Kronecker积的顶点参数,m1 ≤ m2 ≤ ... ≤ mp,2 ≤ p ≤ n, and n ≥ 3 ,扩展了Mamut和Vumar的相关结论[Inform. Process. Lett. 106(2008)258-262].     

基于小波多尺度积的目标识别

光学相关探测就是利用光学相关的方法,从混乱的图像中找出需要的目标,达到识别的目的.把小波变换应用于光电混含联合变换相关器,突破了传统的傅里叶变换的局限性,实现了对探测目标不同区域、不同尺度的分析.为了充分利用小波不同尺度的特性,采用小波多尺度积的方法提取出目标图像的边缘,兼顾了图像的细节与轮廓特征,将目标图像不同层次的轮廓信息和细节信息相结合,解决了复杂背景下目标图像的识别问题.光学实验结果表明,该方法有效增强了复杂背景目标的相关点强度,成功实现了目标的探测,具有良好的应用前景.