一种基于GIS的选址问题及算法

本文考虑了选址区域内存在地理阻断情况下的一种基于GIS的选址问题.对单配送中心选址模型,以GIS返回的任意两点间的最短可行路径的长度作为修正距离函数,分析了目标函数在凸形选址区域上非凸非连续的性质.进一步,采用给出了一种近似搜索算法并通过一个实例计算与重心法进行了比较.     

On topological properties of the Hartman-Mycielski functor

We investigate some topological properties of a normal functorH introduced earlier by Radul which is some functorial compactification of the Hartman-Mycielski construction HM. We prove that the pair (H X, HMY) is homeomorphic to the pair (Q, σ) for each nondegenerated metrizable compactumX and each denseσ-compact subsetY.     

Cyclic Hypomonotonicity,Cyclic Submonotonicity,and Integration

Rockafellar has shown that the subdifferentials of convex functions are always cyclically monotone operators. Moreover, maximal cyclically monotone operators are necessarily operators of this type, since one can construct explicitly a convex function, which turns out to be unique up to a constant, whose subdifferential gives back the operator. This result is a cornerstone in convex analysis and relates tightly convexity and monotonicity. In this paper, we establish analogous robust results that relate weak convexity notions to corresponding notions of weak monotonicity, provided one deals with locally Lipschitz functions and locally bounded operators. In particular, the subdifferentials of locally Lipschitz functions that are directionally hypomonotone [respectively, directionally submonotone] enjoy also an additional cyclic strengthening of this notion and in fact are maximal under this new property. Moreover, every maximal cyclically hypomonotone [respectively, maximal cyclically submonotone] operator is always the Clarke subdifferential of some directionally weakly convex [respectively, directionally approximately convex] locally Lipschitz function, unique up to a constant, which in finite dimentions is a lower C² function [respectively, a lower C¹ function].     

Krylov subspaces and the analytic grade

Typical behaviour of the solution of a linear system of equations obtained iteratively by Krylov methods can be characterized by three stages. Initially the residual diminishes steadily; this is followed by stagnation and finally rapid convergence near the algebraic grade. This study examines this behaviour in terms of the concepts of approximately invariant subspace and what we have called the analytic grade of a Krylov sequence. It is shown how the small Ritz values play a vital role in the convergence and how this knowledge helps in the construction of an effective preconditioner. Copyright © 2004 John Wiley & Sons, Ltd.     

利用计算机辅助装调检测矩形大口径离轴非球面的方法研究

通过非球面的零位补偿法,完成了对矩形大口径离轴非球面镜的检测。先用光学设计软件Zemax从理论上分析了在检测中会出现的现象,并结合计算机辅助装调技术,确定在检测过程中相对敏感的自由度,然后控制这些量,使补偿器和非球面的相对关系与理论设计相吻合,在Zygo相位干涉仪上测得最终结果。在λ=632.8nm时,中心圆口径与两个边缘圆口径面形误差RMS分别为0.022λ,0.037λ,0.032λ。检测结果,达到预期目的。     

Analytical Designing of Two-Aspherical-Mirror Anastigmats Permitting Practical Misalignments in a Soft-X-Ray Optics

A new analytical method of designing two-aspherical-mirror anastigmats was developed and applied to searching solution groups of soft X-ray microscopes of a large misalignment tolerance. The two-mirror anastigmat configurations were expressed by a practical variable related to pupil obstruction limiting the system throughput. Axial coma and other aberrations caused by a slight decenter of the system were then formulated to represent sensitivity to misalignment. These formulations enabled a global survey of solution groups as demonstrated by a designing example of soft X-ray microscopes with a magnification m = −1/50, which resulted in four solutions more insensitive to misalignment than a standard Schwarzschild optics in the soft X-ray region. Some solutions were also found to have much larger fields of view suitable for high resolution imaging as confirmed by computer ray tracing.     

关于非球面制造技术的看法

列举了现代诸高科技领域对非球面光学系统的需求实例，如短波光学，空间光学，红外光学，微电子技术等。然后比较讨论了刀口阴影法与数字干涉检验的优缺点。在非球面修磨方法方面，首先肯定了计算机辅助加工是发展的方向，指出其主要优点在于“失误”造成的反复率大大降低。最后对非球面技术提出了总的看法，并对检测方法和修磨方法提出了几个研究课题。     

高次非球面光路计算中的两个重要问题

提出在高次非球面的光路计算中运用变曲率的“辅助球面”概念,对某些文献在此方面存在的问题进行分析,提出迭代逼近精度的数值判据及浮动处理方法。     

The asphericity of random 2‐dimensional complexes

We study random 2‐dimensional complexes in the Linial–Meshulam model and prove that for the probability parameter satisfying a random 2‐complex Y contains several pairwise disjoint tetrahedra such that the 2‐complex Z obtained by removing any face from each of these tetrahedra is aspherical. Moreover, we prove that the obtained complex Z satisfies the Whitehead conjecture, i.e. any subcomplex is aspherical. This implies that Y is homotopy equivalent to a wedge where Z is a 2‐dimensional aspherical simplicial complex. We also show that under the assumptions where c > 3 and , the complex Z is genuinely 2‐dimensional and in particular, it has sizable 2‐dimensional homology; it follows that in the indicated range of the probability parameter p the cohomological dimension of the fundamental group of a random 2‐complex equals 2. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 261–273, 2015     

轻型高稳定性离轴非球面平行光管设计

为了满足高精度相机在外场环境下的检测要求,采用碳化硅光学材料制作反射镜,碳纤/环氧树脂基复合材料制作遮光筒,设计了一套重量轻、自身精度高、温度稳定性好的离轴平行光管。在二者线胀系数保持二倍关系的情况下,在一定温变范围内保持精度的稳定性。经检测,口径为400 mm,焦距为8 m的离轴平行光管的温变为(20±10)℃,系统波像差为1/5λ(P-V值,λ=632.8 nm)和1/27λ(RMS值),达到了设计要求,能够在外场环境下使用。