一道六边形填数题的改编及解答

文[1]中有如下一题:在六边形的顶点处分别标上数字1,2,3,4,5,6,能否使任意三个相邻顶点上的数字之和大于10?若能,请在图1中标出,若不能,说明理由.文[1]中的解答如下:解析设按要求所填     

On the interaction between dislocations and cracks in one-dimensional hexagonal quasi-crystals

The solution of elasticity problems involving the interaction between dislocations and cracks plays a fundamental role in many practical and theoretical applications. Although elasticity problems involving dislocation or cracks in quasi-crystals have been investigated in many papers, the analysis is limited to a single defect. This paper investigates the interaction of defects in one-dimensional hexagonal quasi-crystals using the complex variable function method. The interaction force between two parallel dislocations is presented and the analytic solutions of elastic fields of interaction between a dislocation and a crack are obtained. A version of the well-known Peach－Koehler formula in one-dimensional hexagonal quasi-crystals is given.     

从窗棂图案到金刚石结构规律探究

笔者研读了一些书籍,体味到了些许科学文化之美,在此与大家分享。最让我心动的还是蜂巢和中国传统的窗棂、漏窗图案之秀美。图1小小的蜜蜂,不愧为是大自然的小精灵,只用正六边形构筑它的巢室,这种构造所用材料最少,构筑成的巢穴空间却最大。花费最少材料,却能获得最大的空间,自然的美妙与数学的简炼和谐之美,紧密地联系在一起。六边形不仅仅在蜂房和艺术的殿堂里找到,在雪花、分子(如苯、已糖及其衍生物)、晶体(如石墨)、海洋生物中都能找到它的倩影。我一边赏析着窗棂图案之美,一边从这些迷人线条组成的复杂背景中梳理着规律性知识。其一,…     

Rayleigh-Marangoni-Benard instability in two-layer fluid system

Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied numerically. The convective instabilities in the system of Silicon Oil (10cSt) and Fluorinert (FC70) liquids have been analyzed. The critical parameters at onset of convection are presented in a large range of two-layer depth ratios from 0.2 to 5.0. Numerical results show that the instability of the two-layer system depends strongly on its depth ratio. When the depth ratio increases, the instability mode changes from mechanical coupling to thermal coupling. Between these two typical coupling modes, a time-dependent oscillation is detected. Nevertheless, traveling wave states are found in the case of oscillatory instability. The oscillation mode results from the competition between Rayleigh instability and Marangoni effect. The project supported by the National Natural Science Foundation of China (10372105) and the Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-SW-L05)     

基于RFID无阻塞扫描控制的机器人室内定位设计

针对RFID移动机器人室内定位中的标签扫描问题,提出一种基于六边形分布模式的RFID无阻塞扫描控制方案,用于机器人的室内定位系统设计和误差检测。首先,将RFID标签根据六边形模式进行分布,减小位置估计的静态误差;然后,阅读器利用固定信道分配(FCA)方法给每个标签分配ID,使阅读范围内标签ID都不相同;最后,当阅读器读取信息时,发送查询请求给范围内的标签,标签根据自身ID决定应答时隙,避免冲突。实验结果表明,相比基于树的扫描控制方案,本文方案能够降低标签/阅读器的复杂度,同时具有较小的位置估计误差和扫描延迟,可帮助机器人实现精确定位。     

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.     

构造“可行域” 例析范围题

"可行域"是指线性规划问题中目标函数z=f(x,y)的自变量x和y的取值区域.线性规划问题在近几年高考中备受青睐,题型从当初的简单、平常到如今的综合、创新,已经不断走向成熟.尤其值得关注的是一些难度较大的综合题,在方法上实现新突破,往往依赖于线性规划的相关知识的正迁移,通过构造"可行域",从而使问题的求解变得柳暗花明.笔者研究近年各省市的高考(模)试题,选择几道范围题赏析"利用可行域"的新解法,权作抛砖引玉.     

辅助线是怎样作出来的

教学教育家波利亚特别强调要教会年青人思考,因此,在学习解题时,要着力弄清楚"这个巧妙的解法是如何想出来的?"赵雪冬、熊月琴老师的这篇文章,较好地体现了波利亚的思想,值得向大家推荐.