Precision Matrix Estimation by Inverse Principal Orthogonal Decomposition

We investigate the structure of a large precision matrix in Gaussian graphical models by decomposing it into a low rank component and a remainder part with sparse precision matrix.Based on the decomposition,we propose to estimate the large precision matrix by inverting a principal orthogonal decomposition(IPOD).The IPOD approach has appealing practical interpretations in conditional graphical models given the low rank component,and it connects to Gaussian graphical models with latent variables.Specifically,we show that the low rank component in the decomposition of the large precision matrix can be viewed as the contribution from the latent variables in a Gaussian graphical model.Compared with existing approaches for latent variable graphical models,the IPOD is conveniently feasible in practice where only inverting a low-dimensional matrix is required.To identify the number of latent variables,which is an objective of its own interest,we investigate and justify an approach by examining the ratios of adjacent eigenvalues of the sample covariance matrix?Theoretical properties,numerical examples,and a real data application demonstrate the merits of the IPOD approach in its convenience,performance,and interpretability.     

The structure and optical properties of AlN nanocrystals prepared by Schlenk techniques at atmospheric pressure and low temperature

AlN nanocrystals were prepared in organic solvent at atmospheric pressure and low temperature by the Schlenk technique. Both hexagonal and cubic AlN nanocrystals were obtained. The hexagonal nano-AlN powder possessed a wurtzite structure with a=3.124 Å, c=5.024 Å, the average grain size was about 2 nm. The lattice constant of the cubic nano-AlN was a=9.171 Å, the average grain size was about 4 nm. The structural and optical properties of the obtained AlN were analyzed. The emission related to deep-level defects was investigated by using temperature-dependent photoluminescence.     

An economic¯X-chart approach to the joint control of the means of independent quality characteristics

Summary In controlling the mean of a multivariate normally distributed quality characteristic the main disadvantage of the globalT ²-control charts is that they don't indicate the component of the quality characteristic which gives rise to an alarm. To avoid this disadvantage the joint use of¯x-charts is proposed in this paper, where — for the sake of simplicity — the investigations are restricted to the case of independent components and to one-sided¯x-charts. On the basis of an economic objective function an approximation to the optimal design of the¯x-charts procedure is derived and discussed. It turns out that at least in the bivariate case the nearly optimal economic design is very close to the exact solution.Supported by the Deutsche Forschungsgemeinschaft (DFG).     

熔融Cu57团簇在急冷过程中弛豫和局域结构转变的分子动力学研究

采用基于嵌入原子方法的正则系综分子动力学研究熔融Cu₅₇团簇在急冷过程中的弛豫及其局域结构变化.通过对弛豫过程中均方位移、非相干中间散射函数和非Gauss参数三种函数和原子键对随急冷温度不同所发生变化的分析表明,在经过短时间的原子剧烈运动后,急冷温度极大地影响着团簇内原子结构弛豫过程.急冷温度较高时,原子在经历短时间剧烈运动的β弛豫后,进入α弛豫区后以扩散运动为主,随后原子运动表现为非扩散性的原子局域结构重排,团簇内没有出现明显的成核结构.随着温度的降低,原子局域结构的变化在经过短时间原子剧烈运动的β弛豫后,在α弛豫区原子运动表现为扩散性运动,并出现一定数量的不稳定二十面体结构.当急冷温度很低时,在进入α弛豫区后,团簇结构变化逐渐表现为非扩散性原子局域结构重排,形成相当数量的稳定成核二十面体结构. 关键词： 团簇 分子动力学 计算机模拟 表面     

新型电感储能脉冲功率驱动源

提出了将传统单个储能电感利用传输线分隔成两部分的新型电感储能脉冲功率驱动源技术方案。理论分析表明,利用传输线电容的耦合延时作用,可有效对调制器输出脉冲波形进行整形,并且可以进一步提高能量转换效率,从而克服传统电感储能脉冲功率源输出波形质量差(类三角波波形)的缺点。基于该思想开展了实验研究,获得了电压约300 kV,电流约20 kA的电子束,并成功驱动S波段磁绝缘线振荡器获得了百MW量级的微波输出。     

氢化硅薄膜光吸收近似特性研究

利用等离子体化学气相沉积系统在直流电压源和射频源的双重激励下,以康宁7059玻璃为衬底制备了氢化硅薄膜．过测定氢化硅薄膜Raman光谱,对薄膜微结构进行了表征;建立氢化硅薄膜的光吸收模型,计算出薄膜的光吸收系数和光学带隙,和实验结果基本一致,说明该模型符合实验结果;并利用该模型计算的光吸收系数和光学带隙,结合AMPS软件对设计的太阳电池结构进行了模拟,给出的I-V特性曲线变化趋势与实验结果基本符合,同时对实验结果与模拟结果存在差异的原因进行了分析,并给出合理解释． 关键词： 氢化硅薄膜 光吸收系数 光吸收模型     

Textbook research in mathematics education: development status and directions

This paper presents a survey study aiming to systematically examine, analyse and review relevant research focusing on mathematics textbooks and hence identify future directions in this field of research. The literature surveyed is selected from different data sources, including mainly journal articles, research theses and conference proceedings. The survey revealed that important progress has been made over the last few decades in mathematics textbook research, though the major achievement has been concentrated in the areas of textbook analysis (including textbook comparison), and the use of textbooks in teaching and learning. It is overall no longer true that the textbook research in mathematics is “scattered, inconclusive, and often trivial” as described six decades ago; however, the development of research on mathematics textbooks has been unbalanced in different areas. Following the review and discussion, the paper proposes five needed directions for advancing the research in this field.     

Operators’s-parameterized ordering and its classical correspondence in quantum optics theory

In reference to the Weyl ordering xmpn→(1/2)mΣι=0m(ιm)Xm-ιPnXι , where X and P are coordinate and momentum operator, respectively, this paper examines operators’s-parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence ((1-s)/2)(n+m)/2Hm,n((2/(1-s))～(1/2)α,(2/(1-s))～(1/2)α)→a+man,and its complementary relation αnα*m→(-i)n+m((1-s)/2)(m+n)/2:Hm,n(i(2/(1-s))～(1/2)a+,i((2/(1-s))～(1/2)a):,where H m,n is the two-variable Hermite polynomial, a, a+ are bosonic annihilation and creation operators respectively, s is a complex parameter. The s’-ordered operator power-series expansion of s-ordered operator sa+mans in terms of the two-variable Hermite polynomial is also derived. Application of operators’s-ordering formula in studying displaced-squeezed chaotic field is discussed.     

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

We newly construct two mutually-conjugate tripartite entangled state representations,based on which we propose the formulation of three-mode entangled fractional Fourier transformation(EFFT) and derive the transformation kernel.The EFFT’s additivity property is proved and the eigenmode of EFFT is derived.As an application,we calculate the EFFT of the three-mode squeezed vacuum state.     

Wavelength beam combining of ytterbium fiber lasers

Wavelength beam combining of five ytterbium fiber lasers is demonstrated in a master-oscillator power-amplifier configuration at combined powers up to 6 W. The combined beam profile has an M2 value of 1.14, which is equal to that of an individual fiber. Beam steering in one dimension over 140 resolvable spots is also demonstrated.