只有一种"足球"的证明

在高二学习多面体欧拉定理时,我遇到了这样一道题目:题:欲制作一个由正六边形和正五边形皮子组成的足球,现有5块六边形皮子,请问需要几块正五边形皮子解:设正五边形皮子的个数为,由多面体欧拉定理F V-E=2知:(5 x) 13(6×5 5x)-21(6×5 5x)=2,解得:x=12,即需要12块正五边形皮子.     

Hexagonal Standing-Wave Patterns in Periodically Forced Reaction-Diffusion Systems

The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2：1 frequency-locking band where the system oscillates at one half of the forcing frequency are examined. An hexagonal standing-wave pattern and other resonant patterns are observed. The detailed phase diagram of resonance structure in the forcing frequency and forcing amplitude parameter space is calculated. The transitions between the resonant standing-wave patterns are of hysteresis when control parameters are varied, and the presence of multiplicity is demonstrated. Analysis in the framework of amplitude equation reveals that the spatial patterns of the standing waves come out as a result of Turing bifurcation in the amplitude equation.     

The dynamic compensation temperature in a kinetic spin-5/2 Ising model on a hexagonal lattice

We present a study of the dynamic behavior of a two-sublattice spin-5/2 Ising model with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on alternating layers of a hexagonal lattice by using the Glauber-type stochastic dynamics.The lattice is formed by alternate layers of spins σ=5/2 and S=5/2.We employ the Glauber transition rates to construct the mean-field dynamic equations.First,we investigate the time variations of the average sublattice magnetizations to find the phases in the system and then the thermal behavior of the dynamic sublattice magnetizations to characterize the nature(first-or second-order) of the phase transitions and to obtain the dynamic phase transition(DPT) points.We also study the thermal behavior of the dynamic total magnetization to find the dynamic compensation temperature and to determine the type of the dynamic compensation behavior.We present the dynamic phase diagrams,including the dynamic compensation temperatures,in nine different planes.The phase diagrams contain seven different fundamental phases,thirteen different mixed phases,in which the binary and ternary combination of fundamental phases and the compensation temperature or the L-type behavior strongly depend on the interaction parameters.     

关于正整数的六边形数部分

对任意正整数n,设b(n)表示n的六边形数部分.即就是b(n)=m(2m-1),如果m(2m-1)≤n＜(m 1)(2m 1),n∈N.本文主要目的是研究一个Dirichlet 级数的收敛性,并给出f(2)的一个精确的计算公式.     

NdF3六边形纳米片的可控合成及发光性能研究

采用水热法,通过调节起始反应溶液中nNd3+/nF-的比值、pH值和螯合剂成功合成了NdF3六边形纳米片.采用X射线衍射(XRD)、扫描电子显微镜(SEM)和透射电子显微镜(TEM)等对合成样品的物相结构及晶粒形态进行了表征,并提出了其可能的生长机制.室温下NdF3六边形纳米片的发射光谱在红外光区904 nm,1066 nm和1330 nm处存在较强的发光峰,最强发射峰位于1066 nm;上转换光谱在522 nm和580 nm处存在较强的发光峰,最强发射峰位于黄光区的580 nm.     

基于三角谐振环的新型六边形谐振环金属线复合周期结构左手材料性质研究

通过实验及仿真研究了三角谐振环组合新型六边形谐振环金属线复合周期结构左手材料.仿真研究了以金属铜三角开口谐振环（SRRs）为基本单元的周期结构负磁导率材料,与闭口环（CSRRs）结果对比发现三角开口谐振环能产生很好的谐振效果即能产生负磁导率,并且多层单元仿真发现多个谐振环耦合能提高谐振频率并加宽谐振频段;设计、制作并实验和仿真研究了三角开口环为基本单元的六边形谐振环金属线复合周期结构左手材料,仿真结果在98GHz附近出现良好负折射效应,实验验证在93—108 GHz出现良好负折射效应,与仿真结果具有良好的一致性.该研究对新型周期结构左手材料的研究、设计和研制具有重要的科学意义和应用前景. 关键词： 左手材料 三角环组成的六边形谐振环 负折射     

氩气/空气介质阻挡放电自组织超六边形斑图实验研究

采用双水电极介质阻挡放电装置,在氩气/空气混合气体放电中,在三种边界条件下得到了一种新型的超六边形斑图.给出了超六边形斑图的傅里叶变换及其不同模强度随旋转角的变化.实验测量了超六边形斑图随空气含量和外加电压变化的相图.研究了超六边形斑图的时空动力学,发现超六边形斑图是由两套子结构嵌套而成.在四边形边界条件下,研究了放电面积的大小对斑图模式选择的影响.发现超四边形斑图的形成受边界条件影响很大,而超六边形斑图则是自组织的结果. 关键词： 介质阻挡放电 超六边形斑图 时空动力学 边界条件     

Optical Properties of Hexagonal and Cubic ZnS Nanoribbons: Experiment and Theory

Optical properties of hexagonal and cubic ZnS nanoribbons are studied by using valence electron energy loss spectroscopy （VEELS） and ab initio band structure calculations. The peaks in VEELS are assigned to interband transitions by comparing the interband transition strengths with the calculated densities of states. The optical properties are deduced from the experimental VEELS, and the theoretical calculations give consistent results. This combination of experimental and theoretical approaches provides a comprehensive understanding of the optical properties of polytype ZnS.     

一种正六边形检测方法的研究

提出了一种基于几何特征的正六边形检测方法。在简述Hough变换原理和正六边形特点的基础上,把正六边形的检测分解成直线和圆的检测,以及线段长度和直线夹角的计算。利用检测到的直线,在图像平面内建立直线方程,依据直线方程,计算相邻两条直线的夹角和交点,求出每条边的长度,同时检测6个交点是否均匀分布在同一圆周上。在螺栓头部正六边形检测实验中,角度测量误差为0.38%,边长测量误差为0.85%。结果表明,该方法是有效的,能准确地检测出图像中的正六边形。     

限制在疏水板中的新的六边形-四边形三层冰结构 (cited: 1)

对限制在两个光滑的疏水板间的水进行了分子动力学模拟,观察到了两种晶体结构,都满足冰规则. 在1 GPa的压强和1.0 nm的板间距下获得的新的冰相是平坦的六边形-四边形三层冰. 在此结构中,靠近板的两层(外层)中的水分子形成六边形环,中间层的水分子形成四边形环. 对于外层的水分子,其四个氢键中的三个在同一层中,另一个氢键与中间层连接. 对于中间层的水分子,四个氢键中的两个在同一层中,而另外两个氢键与两个不同的外层相连. 虽然三层的形状不同,但其面密度却接近相等. 另一种结构是在0.8 nm的板间距和100