矩阵的奇异值与特征值的关系探究及应用

讨论矩阵的奇异值与特征值的关系,并给出奇异值在最优化理论分析中的一个应用.     

N维向量Sturm-Liouville算子的正则迹及其在反谱问题中的应用

研究了赋予一般分离型边界条件的N维向量Sturm-Liouville方程的特征值问题,获得了该系统的一个正则迹公式.迹公式不仅形式美观,而且它在反谱理论中具有重要的作用.     

On a generalization of distance sets

A subset X in the d-dimensional Euclidean space is called a k-distance set if there are exactly k distinct distances between two distinct points in X and a subset X is called a locally k-distance set if for any point x in X, there are at most k distinct distances between x and other points in X.Delsarte, Goethals, and Seidel gave the Fisher type upper bound for the cardinalities of k-distance sets on a sphere in 1977. In the same way, we are able to give the same bound for locally k-distance sets on a sphere. In the first part of this paper, we prove that if X is a locally k-distance set attaining the Fisher type upper bound, then determining a weight function w, (X,w) is a tight weighted spherical 2k-design. This result implies that locally k-distance sets attaining the Fisher type upper bound are k-distance sets. In the second part, we give a new absolute bound for the cardinalities of k-distance sets on a sphere. This upper bound is useful for k-distance sets for which the linear programming bound is not applicable. In the third part, we discuss about locally two-distance sets in Euclidean spaces. We give an upper bound for the cardinalities of locally two-distance sets in Euclidean spaces. Moreover, we prove that the existence of a spherical two-distance set in (d−1)-space which attains the Fisher type upper bound is equivalent to the existence of a locally two-distance set but not a two-distance set in d-space with more than d(d+1)/2 points. We also classify optimal (largest possible) locally two-distance sets for dimensions less than eight. In addition, we determine the maximum cardinalities of locally two-distance sets on a sphere for dimensions less than forty.     

THE REDUCED BASIS TECHNIQUE AS A COARSE SOLVER FOR PARAREAL IN TIME SIMULATIONS

In this paper, we extend the reduced basis methods for parameter dependent problems to the parareal in time algorithm introduced by Lions et al. [12] and solve a nonlinear evolutionary parabolic partial differential equation. The fine solver is based on the finite element method or spectral element method in space and a semi-implicit Runge-Kutta scheme in time. The coarse solver is based on a semi-implicit scheme in time and the reduced basis approximation in space. Of[line-online procedures are developed, and it is proved that the computational complexity of the on-line stage depends only on the dimension of the reduced basis space （typically small）. Parareal in time algorithms based on a multi-grids finite element method and a multi-degrees finite element method are also presented. Some numerical results are reported.     

Theoretical characterization of axial deformation effects on hydrogen storage of Ti decorated armchair (5,5) SWCNT

Theoretical calculations have been performed in the framework of density functional theory to characterize the effect of axial deformation on hydrogen storage of Ti decorated armchair (5,5) SWCNT. The theoretical characterization has been carried out in terms of H₂ adsorption energies that are lying in the desirable energy window (?0.2 to ?0.6?eV) recommended by DOE, as well as a variety of physicochemical properties. A remarkable and significant change in H₂ adsorption energy is observed under the effect of only (1%) axial strain. Axial relaxation leads to H₂ adsorption energies within the recommended energy range for hydrogen storage, in contrast to axial compression. Simultaneous weakening of π and σ interactions, due to the effect of axial relaxation and loss of spatial orbital overlap, is in favor of hydrogen adsorption in the recommended energy range, and dominates the effect of charge transfer from Ti 3d to C 2p of the SWCNT. The calculated pairwise and non pairwise additive components confirm that the role of the SWCNT is not restricted to supporting the metal. Polarizability and hperpolarizabilty calculations as well as spectral analysis characterize the relaxed structure (Z?=?1.02), for which H₂ adsorption energy (?0.34?eV) is in the recommended energy range for hydrogen storage, to be energetically more preferable than the compressed structure (Z?=?0.99). The results offer a way to control and characterize the hydrogenation process of metal functionalized SWCNTs by strain loading.     

大气波导条件下雷达海杂波功率仿真

考虑近海面大气折射率垂直梯度的变化, 采用曲面波频谱估计方法(CWSE)计算掠射角, 并结合修正的GIT海表反射率模型和雷达距离方程对大气波导条件下雷达海杂波功率进行仿真, 最后通过数值实验及与实测数据比较, 验证了CWSE方法的可行性. 关键词： 大气波导 雷达海杂波 曲面波频谱估计     

连续氙灯发光光谱的设计与应用研究

对太阳实际光谱与连续氙灯的光谱进行了测试,结果显示氙灯发光光谱的红外部分占全部光谱的55.6%,与实际太阳光谱的28.4%有较大差别。依据这种差别进行光谱曲线拟合,得到925 nm最低点的透过率曲线。采用滤光片对氙灯发光光谱的红外部分光强进行适当过滤,测得过滤后的光谱达到标准匹配度。通过测试滤光后6个不同位置点的光谱发现,光谱最大偏差仅为12.5%,表明过滤后的氙灯光谱均匀性较好。利用电致发光检测有缺陷的硅电池进行电池的电性能测试,发现经过采用滤光片和未采用滤光片的连续氙灯光照测试的Ⅰ-Ⅴ电性能值不同,功率相差0.22 W,表明氙灯光谱匹配度直接影响电池电性能测试的准确度。     

组合几何蒙特卡罗粒子输运支撑软件框架JCOGIN介绍

介绍了JCOGIN支撑软件框架层次式、模块化的体系结构及其核心数据结构。这些使得JCOGIN软件框架能够支撑大规模复杂几何的蒙特卡罗（MC）粒子输运并行计算。同时介绍了在JCOGIN支撑软件框架下研发的JMCT程序,并进行了性能测试,在2万处理器核上模拟20亿粒子,并行效率达到70%。     

非下采样小波变换红外光谱数据去噪

为了降低噪声对实测红外光谱信号的影响,引入了一种非下采样小波变换的红外光谱数据去噪方法。采用非下采样小波变换对原始光谱信号进行多尺度分解,提取信号的多尺度细节特征;根据光谱信号和噪声在不同尺度上的差异,通过应用变分偏微分方程方法调整分解后的各子带系数;重构各子带就可以将原始光谱信号中真实信号和噪声分离,从而达到剔除噪声的目的。通过两组实验对比传统小波和该方法针对红外光谱数据的消噪效果,实验结果表明:非下采样小波变换在红外光谱数据去噪方面具有明显的优势,不仅能够有效地去除噪声,很好地保持信号的形状,并且均方误差较小;在实际的红外光谱数据处理中能够获得较好的去噪效果。     

Nematics in Hybrid Cylindrical Cells

A hybrid (weak-strong anchoring) cylindrical cell with antagonistic boundary conditions (planar–homeotropic) at the outer confining surface and at a central coaxial cylindrical core and filled with nematic liquid crystals is investigated by means of the Elastic Theory and Monte Carlo Simulations. The director orientation profile on the surface characterized by weak anchoring is built as a function of the extrapolation length and other relevant parameters. By considering the angle on the surface as an order parameter, a transition in the orientation is found when the extrapolation length becomes smaller than a critical value and the orientation of the surface with strong anchoring is dominant. The order parameter critical exponent is numerically calculated, and the mean field value (β≈1/2) is found in all cases. These transitions are essentially confirmed by Monte Carlo simulations even if some numerical discrepancies are found. The analysis show similarities between planar and cylindrical geometries, but non-usual consequences are found more easily in the latter one.