Ringel对偶代数的三角分解

本文证明了树型偏序集的扭双指标代数的Ringel对偶代数存在三角分解,并具体给出了一种三角分解的结构,     

一类具有非线性发生率和治疗函数的传染病模型研究

传染病动力学系统的数学建模中,合理的使用非线性发生率往往更能使模型与实际相吻合.并且在实际的疾病防治过程中,由于受到空间人力物力资源的影响一般存在最大治疗容量的限制.结合这两种情况建立了一类含非线性发生率和最大治疗容量限制的传染病模型.通过分析这个模型,得到无病平衡点和正平衡点的存在性、稳定性.进一步取发生率和治疗系统达到最大容量时的感染者人数作为分支参数,得到了Hopf分支和Bogdanov-Takens分支的存在条件,并进行了数值模拟.     

硬X射线微束掠入射实验的控制和数据采集系统及其应用

在国内发展了硬X射线微束掠入射实验方法,并将此具有微米级高空间分辨率的方法应用于纳米厚度薄膜的微区分析。该实验方法对分析样品表面或薄膜在微小区域的不均匀组分、结构、厚度、粗糙度和表面元素化学价态等信息具有重要意义。基于X射线全反射原理,以微聚焦实验站的高通量、能量可调的单色微束X射线为基础,通过集成运动控制、光强探测、衍射和荧光探测,设计了掠入射实验方法的控制和数据采集系统。此系统采用分布式控制结构,并基于Experimental Physics and Industrial Control System （EPICS）环境设计SPEC控制软件。通过建立SPEC和EPICS的访问通道,实现SPEC软件对EPICS平台上设备的控制和数据获取。在所设计的控制和数据采集系统中,运动控制系统控制多维样品台电机的运动,实现定位样品位置和调节掠入射角;光强探测系统则监测样品出射光强度,通过样品台运动控制和光强探测的联控,实现样品台的扫描定位控制;通过衍射和荧光探测系统获取不同入射深度下样品的衍射峰强度和荧光计数。此外,为准确控制掠入射角角度,必须确定样品平面与X射线平行的零角度位置,对此给出一种自动定位零角度的方法,编写了该方法的控制算法,设计了相应的控制软件。零角度自动化定位的扫描结果表明,实验系统微区分析的空间分辨率达到2.8 μm,零角度定位精度小于±0.01°。利用该系统在上海光源微聚焦实验站首次实现了具有自动化准确控制零角度的微束掠入射X射线衍射和荧光同步表征的实验方法,实验中被测样品为10 nm Au/Cr/Si薄膜材料,Si基底最上层为10 nm厚的Au薄膜,其间为一层很薄的Cr粘附层。在不同掠入射角下测量样品的衍射信号,获取不同入射深度下样品的衍射峰强度,并实现在同一掠入射角下,同步采集样品的荧光计数信号,从而确定了样品表层的相结构信息以及荧光信号强度与入射角关系,实现了对纳米厚度薄膜在微小区域的相结构和组分分析。此外,通过该技术能够选取荧光计数最大值对应的入射角度,有助于提高后续发展的低浓度样品掠入射X射线吸收近边结构实验方法的信噪比。     

Some peculiarities for grazing incidence neutron diffraction from 3D near-surface nanostructures

Neutron diffraction at grazing incidence was simulated for the regularly ordered nanostructures on the surface and in the near-surface volume of a homogeneous matrix. Silicon was used as a matrix material and nanoparticles consisting of gold or nickel. This allowed obtaining a good scattering contrast between the matrix and nanoparticles and, as a result, high contrast diffraction patterns. It is shown that the modified kinematic approximation which takes into account the refraction of a neutron wave at the interface makes it possible to obtain a reasonable agreement with the available experimental data. In addition, it was demonstrated that in contrast to the traditional diffraction on point-like scattering centers, some unusual systematic absences could be observed due to the experiment geometric conditions and the finite geometric sizes of the nanoparticles. The results demonstrate that modified kinematic approximation can be successfully used to model non-specular neutron scattering from near-surface nanostructures and thereby facilitate the interpretation of experimental results.     

周视大像旋稳海天线向量角补偿算法

为使两轴周视光电探测系统在三自由度扰动和大像旋条件下搜索并跟踪水面目标,在虚拟天际线焦平面像五自由度解析表达式基础上,推导出焦平面坐标系铅直轴的方向向量和该坐标系下海天出射平面法向量夹角的余弦表达式.该式求反余弦后减π/2,得到焦平面铅直坐标轴的方向向量和海天出射平面法向量小于π/2的夹角,该夹角的0.5倍作为俯仰反射镜的净作动量,目的是克服非线性像旋使包含目标信息的虚拟海天线的像线通过焦平面中心.该算法与方位补偿算法联动能够使目标像点始终逼近焦平面原点.通过数学模型仿真和真实工况试验都验证了俯仰机构位置环海天线向量角补偿算法的合理性.     

不完备信息下的灰色粗糙集成决策模型侯亚林

In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.     

Crystal orientation in poly(ethylene 2,6-naphthalate) ultrathin films revealed by reflection-absorption infrared spectroscopy and grazing incidence X-ray diffraction

Crystal orientation of poly(ethylene 2, 6-naphthalate) (PEN) ultrathin films was investigated by the combination of reflection-absorption infrared spectroscopy (RAIR) and grazing incidence X-ray diffraction (GIXD) techniques. It is concluded that the main-chain of PEN molecule in ultrathin film is prone to alignment parallel to the substrate when compared with thicker films. During the formation of α form crystalline, the naphthalene ring, the CO group in molecular chain of PEN as well as the b axis in crystalline tend to take orientation more parallel to the substrate due to the surface-induced effect. However, such an anisotropic structure could not be observed in the bulk PEN.     

Design of wideband graded-index antireflection coatings at oblique light incidence

We suggest a design method of graded-refractive-index (GRIN) antireflection (AR) coating for s-polarized or p-polarized light at off-normal incidence. The spectrum characteristic of the designed antireflection coating with a quintic effective refractive-index profile for a given state of polarization has been discussed. In addition, the genetic algorithm was used to optimize the refractive index profile of the GRIN antireflection for reducing the mean reflectance of s- and p-polarizations. The average reflectance loss was reduced to only 0.04% by applying optimized GRIN AR coatings onto BK7 glass over the wavelength range from 400 to 800 nm at the incident angle of θ₀ =70°.     

玻璃基底Wolter-1型X射线聚焦镜研制及测试

Wolter-1型X射线聚焦镜可将掠入射的X射线反射至焦平面处,具有较强的成像探测能力,在天文探测等领域中具有重要作用.通过建立几何模型对反射镜面及反射光线方程进行理论计算,推导出了适用于以玻璃为基底材料的聚焦镜设计参数方程,可用于对此类聚焦镜进行理论设计,依据理论设计,采用具有极高表面光洁度的超薄肖特D263T玻璃经热弯成型后作为反射镜基底,在反射镜表面制备金属铱薄膜作为反射膜研制了Wolter-1型反射镜组,并使用激光三维扫描仪对所研制的聚焦镜片面型进行了测试.测试结果显示,实际镜片面型与理想镜片面型公差在10 μm以内的测试点占总测试点的50%.通过搭建可见光条件下的焦斑测试系统,使用图像采集相机采集焦斑的灰度图像,通过图像分析软件分析计算该灰度图像的灰度分布来定量分析焦斑的能量分布情况,从而确定焦斑特性参数.实验结果显示：研制出的聚焦镜片焦距为1.6 m,焦斑的半能量包围直径为0.33 mm,对应角分辨率为0.7角分.     

光锥角对窄带滤光片透射率的影响及补偿方法

全介质膜窄带滤光片因具有优良的光学性能、较强的工艺性和空间环境适应性被广泛应用于空间多光谱遥感仪器中,但锥光束入射导致的中心波长漂移问题严重影响此类窄带滤光片的光谱选择性能。为了研究光锥角对窄带滤光片透射率特性的影响,设计了非规整型全介质膜窄带滤光片,分析了高斯光束倾斜入射窄带滤光片导致透射率的变化,建立了非均匀照度下锥光束正入射时窄带滤光片等效透射率的求解模型,定量求解了等效透射率及中心波长漂移量,并对理论模型进行了实验验证。结果表明,锥光束正入射对窄带滤光片透射率的影响主要表现为中心波长的蓝移;在镀膜工艺相对稳定的基础上,理论模型的等效透射率预测精度优于中心波长的0.15%。所以,可以使用等效透射率求解模型定量计算锥光束正入射导致窄带滤光片透射率的变化,并利用中心波长漂移量修正后的设计数据指导滤光片镀膜,进而实现窄带滤光片的高精度光谱选择,这为解决介质膜窄带滤光片因锥光束入射导致的中心波长漂移问题提供了新的技术途径。