阴极荧光光谱有效收集效率的计算与测量（I）

从点光源均匀发光模型出发,重点导出了回转半椭球面镜的阴极荧光(Cathodoluminescence,简称CL)光谱有效收集效率η_λ~(eff)的计算公式,分析讨论了收集效率η_λ~(eff)与椭球参数e、收集角、Δφ出射角Δ(?)以及出射光束方位角θ_N的关系,给出了相应的理论计算和模拟实验结果.研究表明,理论计算与实验结果一致.     

高能量密度激光器腔镜有限元分析

 通过对高能量密度激光器运行过程中腔镜存在的表面及背面吸收热量的有限元分析,得出腔镜表面在不同吸收热流密度和约束条件条件下热变形分布。指出提高腔镜反射率,改变腔镜的基底材料以及优化腔镜的约束条件是显著降低腔镜反射面变形的有效途径。     

大口径轻型红外扫描镜技术的研究

分析了大口径轻型红外扫描镜国内研制的必要性。讨论了国内的研制方案。研究了关键技术的现状 ,并对未来发展进行了展望。     

不变性在线性代数中应用两例

本文介绍数学中“不变性”思想，讨论了线性代数中某种条件下秩数不变、特征多项式、特征值不变；对称性、半正定、正定性不变；以及度量性不变．以初等变换为首要方法，解决线性代数中一类重要问题．阐述了矩阵或线性方程组线性变换的本质     

Malliavin's theorem for weak synthesis on nonabelian groups

Malliavin's celebrated theorem on the failure of spectral synthesis for the Fourier algebra A(G) on nondiscrete abelian groups was strengthened to give failure of weak synthesis by Parthasarathy and Varma. We extend this to nonabelian groups by proving that weak synthesis holds for A(G) if and only if G is discrete. We give the injection theorem and the inverse projection theorem for weak X-spectral synthesis, as well as a condition for the union of two weak X-spectral sets to be weak X-spectral for an A(G)-submodule X of VN(G). Relations between weak X-synthesis in A(G) and A(G×G) and the Varopoulos algebra V(G) are explored. The concept of operator synthesis was introduced by Arveson. We extend several recent investigations on operator synthesis by defining and studying, for a V^∞(G)-submodule M of B(L²(G)), sets of weak M-operator synthesis. Relations between X-Ditkin sets and M-operator Ditkin sets and between weak X-spectral synthesis and weak M-operator synthesis are explored.     

The structure of Valdivia compact lines

We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed ℵ₁, every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author.     

Periodic points of solvable group actions on 1-arcwise connected continua

It is shown that every continuous action of a solvable group on a 1-arcwise connected continuum must have a fixed point or have a 2-periodic point.     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

Towards an ‘average’ version of the Birch and Swinnerton-Dyer conjecture

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The Birch and Swinnerton-Dyer conjecture states that the rank of the Mordell-Weil group of an elliptic curve E equals the order of vanishing at the central point of the associated L-function L(s,E). Previous investigations have focused on bounding how far we must go above the central point to be assured of finding a zero, bounding the rank of a fixed curve or on bounding the average rank in a family. Mestre (1986) [Mes] showed the first zero occurs by , where NE is the conductor of E, though we expect the correct scale to study the zeros near the central point is the significantly smaller . We significantly improve on Mestre's result by averaging over a one-parameter family of elliptic curves E over Q(T). We assume GRH, Tate's conjecture if E is not a rational surface, and either the ABC or the Square-Free Sieve Conjecture if the discriminant has an irreducible polynomial factor of degree at least 4. We find non-trivial upper and lower bounds for the average number of normalized zeros in intervals on the order of (which is the expected scale). Our results may be interpreted as providing further evidence in support of the Birch and Swinnerton-Dyer conjecture, as well as the Katz-Sarnak density conjecture from random matrix theory (as the number of zeros predicted by random matrix theory lies between our upper and lower bounds). These methods may be applied to additional families of L-functions.

Video

For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=3EVYPNi_LG0.     

Estimation of means of multivariate normal populations with order restriction

Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restriction for vector valued parameters. Two cases of estimating multivariate normal means under order restricted set are considered. One case is that covariance matrices are known, the other one is that covariance matrices are unknown but are restricted by partial order. This paper shows that when covariance matrices are known, the estimator given by this paper always dominates unrestricted maximum likelihood estimator uniformly, and when covariance matrices are unknown, the plug-in estimator dominates unrestricted maximum likelihood estimator under the order restricted set of covariance matrices. The isotonic regression estimators in this paper are the generalizations of plug-in estimators in unitary case.