Center and isochronous center problems for quasi analytic systems

This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The convergence of first integral near the center is proved. Using the general results to quasi-quadratic systems, the problem of the isochronous center of the origin is completely solved. This research is partially supported by the National Natural Science Foundation of China (10671179 and 10771196) and the Natural Science Foundation of Yunnan Province (2005A0092M)     

Probabilistic analysis of geometric location problems

We analyze the behaviour of thek center and median problems forn points randomly distributed in an arbitrary regionA ofR ^d . Under a mild assumption on the regionA, we show that fork≦k(n)=o(n/logn), the objective function values of the discrete and continuous versions of these problems are equal to each otheralmost surely. For the two-dimensional case, both these problems can be solved by placing the centers or medians in an especially simple regular hexagonal pattern (the ‘honeycomb heuristic’ of Papadimitriou). This yields the exact asymptotic values for thek center and median problem, namely, α(|A|/k)^1/2 and β(|A|/k)^1/2, where |A| denotes the volume ofA, α and β are known constants, and the objective of the median problem is given in terms of the average, rather than the usual total, distance. For the 3- and 4-dimensional case, similar results can be obtained for the center problem to within an accuracy of roughly one percent. As a by-product, we also get asymptotically optimal algorithms for the 2-dimensionalp-normk median problem and for the twin problems of minimizing the maximum number of vertices served by any center and similarly for maximizing the minimum.     

Luminescent polymers with discrete emitter units

Optical absorption and photo-luminescence measurements were performed on a series of semiconducting polymers, based upon phenylene linkages, that have discrete emitter units. In these polymers, broken conjugation has been achieved in two ways: by introducing metalinkages between various numbers of para-connected aromatic groups or by severe steric distortion of a fully conjugated main chain. In either case, electronic states are localized on relatively small units, resulting in a large (π, π^*) band gap. The band gap decreases with increasing emitter unit conjugation, as expected. Blue light emission was observed from these materials, with the peak emission wavelength red shifted (by greater than 1 eV on average) from the peak absorption. © 1994 John Wiley & Sons, Inc.     

Chapter 6 On the construction of strong complementarity slackness solutions for DEA linear programming problems using a primal-dual interior-point method

A novel approach for solving the DEA linear programming problems using a primaldual interior-point method is presented. The solution found by this method satisfies the Strong Complementarity Slackness Condition (SCSC) and maximizes the product of the positive components among all SCSC solutions. The first property is critical in the use of DEA and the second one contributes significantly to the reliability of the solution.This research was partially supported by NSF Cooperative Agreement No. CCR-88-09615, ARO Grant 9DAAL03-90-G-0093, DOE Grant DEFG05-86-ER25017, and AFOSR Grant 89-0363.Partially supported by Fulbright/LASPAU.     

BaF2中Vk心的ESR谱分析

电子自旋共振（ＥＳＲ）实验间接表明，γ射线辐照能在室温下在ＢａＦ２微晶中产生Ｆｒｅｎｋｅｌ激子这样的元激发，此元激发受热在１５０℃以下消失。γ射线辐照使ＢａＦ２微晶中Ｆ－离子上的２Ｐ电子跃迁到外层轨道，并与２Ｐ轨道的空穴形成紧束缚的电子－空穴对——Ｆｒｅｎｋｅｌ激子。激子中的电子受热脱离Ｆ原子，这种晶格上的Ｆ０是ＥＳＲ可探测的顺磁色心点缺陷——Ｖｋ心。受γ射线辐照的ＢａＦ２微晶中含有Ｆｒｅｎｋｅｌ激子，受热时Ｆｒｅｎｋｅｌ激子湮灭。Ｖｋ心增多的现象，表现为随温度增高Ｖｋ心的ＥＳＲ信号增强的反常现象。     

刚体绕瞬心的转动方程的计算机模拟

在《大学物理》上曾对刚体绕瞬心的转动方程进行过广泛深入的讨论，这些讨论都是建立在解析分析的基础上，本则用计算机模拟的方法研究这个方程．计算机模拟的结果不仅形象直观地表现了公式的丰富内涵，也证明计算机模拟是教学研究的一种优秀工具．     

高能强子－核作用中快度分布与横能的关联

假定强子－核作用中的产生粒子相对于反应体质心系各向同性衰变，给出了强子－核作用中横能快度分布，计算结果能够解释最新的ＨＥＬＩＯＳ合作组的实验结果．     

碘化铯晶体中电子型色心的电子结构研究

运用以密度泛函理论为基础的相对论性离散变分方法(DV-Xα)模拟计算了完整的和含有F心、F+心以及F2心的碘化铯(CsI)晶体的电子结构,得到了含F心和F+心以及F2心的CsI晶体电子态密度分布以及它们可能产生的光学跃迁模式.计算结果表明,含F心和F2心的CsI晶体的禁带宽度明显变窄,F心和F2心的能级都出现在禁带中并且作为施主能级位于导带底部,利用过渡态理论计算得到其能级向Cs的5d轨道发生光学跃迁,能量跃迁值分别为1.69eV和1.15eV,该结果与实验结果完全一致,F+心没有能级出现在禁带中.计算结果从理论上成功地解释了碘化铯晶体经过辐照后电子型色心所产生的吸收带起源问题.     

LAMOST光纤单元定位参数研究

大天区多目标光纤光谱天文望远镜LAMOST是世界上光谱获取量最大的望远镜,4000个双回转光纤单元的精确定位是关键因素之一。根据对星像观测的要求以及单元的定位方式,确立了所需的7个定位参数,研究了在复杂现场环境下获取定位参数的具体流程和可行性算法,包括光重心法、摄像机快速标定算法、基于最小二乘拟合圆算法、空间坐标旋转算法等。通过模拟星像观测仿真测试和现场星像试观测证明,定位参数精度能很好地满足观测需求。目前LAMOST望远镜观测光谱获取率已达到90%以上。