On a relation between spectral theory of lens spaces and Ehrhart theory

In this article Ehrhart quasi-polynomials of simplices are employed to determine isospectral lens spaces in terms of a finite set of numbers. Using the natural lattice associated with a lens space the associated toric variety of a lens space is introduced. It is proved that if two lens spaces are isospectral then the dimension of global sections of powers of a natural line bundle on these two toric varieties are equal and they have the same general intersection number. Also, harmonic polynomial representation of the group SO($n$) is used to provide a more elementary proof for a theorem of Lauret, Miatello and Rossetti on isospectrality of lens spaces.     

On the number of invisible directions for a smooth Riemannian metric

In this note we give a construction of a $C^{\infty }$-smooth Riemannian metric on $R^n$ which is standard Euclidean outside a compact set $K$ and such that it has $N=n(n+1)/2$ invisible directions, meaning that all geodesic lines passing through the set $K$ in these directions remain the same straight lines on exit. For example in the plane our construction gives three invisible directions. This is in contrast with billiard type obstacles where a very sophisticated example due to A. Plakhov and V. Roshchina gives 2 invisible directions in the plane and 3 in the space.We use reflection group of the root system $A_n$ in order to make the directions of the roots invisible.     

Object reconstruction in scattering medium using multiple elliptical polarized speckle contrast projections and optical clearing agents

In this paper, we present a hybrid method for improving the imaging quality of objects obscured within a scattering environment by combining multiple elliptical polarized speckle contrast projections with the use of optical clearing agents (OCAs). Elliptically polarized light enables the probing of subsurface volumes, where OCAs decrease light scattering while increasing photons׳ penetration depth through the medium. Experiments were conducted on object sample and prostate cancer cells embedded within ex vivo biological samples (chicken breasts) in reflection configuration. After immersion with OCAs, the medium was irradiated with an elliptically polarized laser beam and multiple polarized speckled images obtained from a lens array were first converted to speckled contrast images and then processed using a self-deconvolution shift-and-add algorithm. The conversion to contrast images and multiple perspectives acquisition was found to emphasize contrast. Analysis of image quality indicated improvement in object visualization by the combination of elliptical polarization and OCAs. This enhanced imaging strategy may advance the development of improved methods in biomedicine field, specifically biomedical tomography.     

神光Ⅲ核心X射线分幅相机(英文)

神光III装置核心X射线分幅相机将用于激光装置性能验收实验和宽范围的高能量密度物理、惯性约束聚变物理及基础物理实验研究.相机系统主要为记录神光III装置靶的时间分辨X射线发射设计,利用可更换的鼻椎实现具有二维空间分辨或者一维谱分辨的靶形貌时间分辨图像.神光III装置核心X射线分幅相机将被嵌入到一个铝制空气包中,空气包具有大容量冷却平板和一个特制的环境监测传感器阵列.相机设计很多部分不同于早期X射线分幅相机,如一套全新的阻抗匹配方案,曝光时间从0.07-1.5ns可调,先进的荧光屏,脉冲屏压电路,准确的模块定位,独特的监控系统和完全远程计算机控制.其中先进的荧光屏和脉冲屏压电路已经获得初步应用.     

Multiple vertex coverings by specified induced subgraphs

Given graphs H₁,…, H_k, let f(H₁,…, H_k) be the minimum order of a graph G such that for each i, the induced copies of H_i in G cover V(G). We prove constructively that f(H₁, H₂) ≤ 2(n(H₁) + n(H₂) − 2); equality holds when H₁ = H ₂ = K_n. We prove that f(H₁, K _n) = n + 2√δ(H₁)n + O(1) as n → ∞. We also determine f(K_{1, m −1}, K _n) exactly. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 180–190, 2000     

50°视场角投影式头盔光学系统设计及逆反射屏研究

设计了一款适于医疗培训用投影式头盔物镜系统,出瞳直径8 mm,视场50°,能够满足对角0.9英寸微显示器对超高分辨SXGA模式的显示要求.其结构紧凑,口径10 mm,长度12 mm,重量仅有5 g.本物镜系统场曲仅0.35 D,畸变仅0.64%.为考察本投影式头盔系统的成像特性,研究了不同“逆反射材料”的特性.实验得到高强级逆反射材料在±40°视场范围内反射光强无明显变化,适合做为投影屏幕材料.定量分析了逆反射屏放置位置对成像的影响.     

Homogeneous Embeddings of Cycles in Graphs

If G and H are vertex-transitive graphs, then the framing number fr(G,H) of G and H is defined as the minimum order of a graph every vertex of which belongs to an induced G and an induced H. This paper investigates fr(C _m,C _n) for m<n. We show first that fr(C _m,C _n)≥n+2 and determine when equality occurs. Thereafter we establish general lower and upper bounds which show that fr(C _m,C _n) is approximately the minimum of and n+n/m. Received: June 12, 1996 / Revised: June 2, 1997     

A Spectrometer Based on Diffractive Lens

A novel spectrometer is designed based on diffractive lens. It is essentially a flat field spectrometer. All the focal points are along the optical axis. Besides, all the asymmetrical aberrations vanish in our mounting. Thus low aberration can be obtained. In this article a diffractive lens is modeled as a special grating and analyzed by using a grating-based method. And a stigmatic point is introduced to reduce the aberrations.     

物镜象差对分辨率影响的一种测量分析法

物镜的分辨率除受入射波长、照明相干度和物镜的数值孔径影响外,很大程度上还受物镜象差的影响.本文提出了一种定性分析测量物镜象差和加工装配误差对分辨率的综合影响的新方法,利用该方法对两不同物镜象差影响进行测试和分析并用这两物镜进行了曝光光刻试验,光刻试验的结果和测量分析的结果相吻合.     

用于变象管测量的Nd:YAG激光器倍频系统

本文叙述了一种新型的Nd:YAG激光器倍频系统,它主要用于诊断皮秒扫描/分幅变象管的静态及动态特性,亦可用于非线性光学和其它超快现象。最后讨论了影响谐波器件转换效率的一些参数。通过计算机模拟确定了这些参数的最佳值,从而使谐波器件的转换效率得到进一步提高。