数学竞赛中的一道光学题探索

2007年浙江省宁波市初二数学竞赛第二试第3题:有两面可绕一立轴转动的立式镜,我站在这两面镜子前的一个点上,这个点位于镜面夹角平分面上.若两镜面的夹角为50°,我将可以看到自己的镜像数为()     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

与抛物线相关的一类正三角形的个数问题——由2011年高考数学湖北卷的一道选择题所引发的探究

2011年高考数学湖北卷文、理科选择题中有如下一题:记满足两个顶点在抛物线y2=2px(p＞0)上,另外一个顶点是抛物线的焦点的正三角形个数为n,则A.n=0 B.n=1 C.n=2 D.n≥2这道题以与抛物线相关的正三角形为问题情境,主要考查直线与抛物线的位置关系和数形结合的思想.要求考生能通过几何直观,并抓住满足条件的正三角形和抛物线分别关于x轴对称的特征,进行合情推理,容易得出正确选项为C.     

Surface plasmon interference formed by tightly focused higher polarization order axially symmetric polarized beams

We numerically study the surface plasmon interference formed by tightly focused higher polarization order axially symmetric polarized beams (ASPBs) based on the vectorial diffraction theory. The definition of ASPBs is stated, and the optical setup for surface plasmon polariton (SPP) excitation and mathematical expressions for interfering SPP fields are proposed. The simulation results show that the interfering SPP fields present a multi-focal spot pattern. In addition, the number of spots is related to the polarization order of the incident beams P as 2×(P-1), indicating potential utilization in near-field multiple optical trapping and near-field imaging and sensing. The unique interfering phenomenon is also explained.     

圆的有关性质

中考要求 1.理解圆及其有关概念,了解弧、弦及圆心角之间的关系,探索并了解点与圆、直线与圆以及圆与圆的位置关系. 2.探索圆的性质,了解圆周角与圆心角的关系、直径所对圆周角的特征. 考点1 轴对称(垂径定理及推论) 考点2圆心角、弧、弦、弦心距之间的关系 考点3圆周角的定理及推论 考点4圆内接四边形的性质     

二维轴对称图象高阶胡氏不变矩快速算法的改进

提出了基于二维轴对称性目标图象矩快速算法的实用化改进方案.算法实用化改进是通过两个命题的证明实现的.一是通过轴对称目标图象质心在对称轴上的命题证明,实现了将二维轴对称图象矩快速算法用于轴对称性图象中心矩的计算;二是通过目标图象以坐标系中任意两点为圆心,旋转相同角度,结果图象具有平移性的命题证明,实现了算法用于对旋转不同角度的对称目标图象的中心矩的计算改进.在此基础上,完成了二维轴对称目标图象高阶胡氏不变矩实用化快速算法的实现.实验证明,该算法具有较好的实时性能,且具有较小的引入误差.     

Mechanism for Influence of Nose Bluntness on Asymmetric Vortices

Pressure distributions on slender bodies are measured at various roll angles; it is found that the side loads on the blunted-nose slender body are as small as one-third of that on a pointed-nose one, or even zero at some roll angles. Numerical simulation shows that different flow structures are generated on the leeside of the bodies with different noses. The results confirm that a structure of U-shaped horseshoe vortex develops on the top of the blunted nose due to the closed type of surface flow separation. The shear layer separated from the nose is entrapped into the horseshoe vortex core and forms two mainof this structure is to hold in the two main nose vortices andvortices on the two sides of the body. The function to restrict the emergence of asymmetry.