相依回归系统的主成分改进估计

对两个相依方程组成的回归系统,当设计矩阵呈病态时,提出了回归系数的一个主成分估计β_1**(k)及其相应的两步估计β_1**(k,T),并在均方误差意义下研究了它们的优良性质。     

牙齿磷光检测技术研究

本文分析了牙齿磷光测量技术一直不能进一步发展的原因,提出了一种新的检测技术。这种技术利用光纤传输紫外光和磷光,利用光电接收器作为传感器,解决了牙齿磷光现象一直不能定量分析的问题,使得牙齿磷光现象与牙齿疾病之间关系的研究得到了进一步的发展。     

Conjectures on the character degrees of the harada-norton simple group HN

We classify the radical subgroups and chains of the Harada-Norton simple group HN and verify the Alperin weight conjecture and the refined Dade conjecture due to Uno for the group. This implies the Isaacs-Navarro and Dade reductive conjectures for the group. This work was supported in part by the Marsden Fund of New Zealand via grant #9144/3368248.     

A flexible and high-performance bidirectional optical amplifier with all optical gain control using ASE noise path through multi-port circulators

We report a flexible all-optical gain controlled bidirectional optical amplifier. The device achieves constant gain and low noise figure over a large input power range. Moreover, the device removes Rayleigh backscattered light and amplifier noise.     

Improvement of polyacrylate coating by filling modified nano-TiO2

Nano-TiO₂ is modified by a method, by which nano-TiO₂ first reacts with silane coupling agent WD-70 with double bond group which subsequently copolymerizes with methyl methacrylate and butyl acrylate to produce a thin polymer shell on the nanoparticles. The modified nanoparticles have stable organophilicity. They are applied to polyacrylate coating and performances of the coating are measured by different methods. The modification of nano-TiO₂ particles can improve their dispersibility in coating, enhance hardness of coating and reduce water absorption and permeability of polyacrylate coating. The mechanism has been analyzed in this paper.     

On scattering of electromagnetic radiation by inhomogeneities of the velocity of motion of the medium

Analysis of the scattering of a plane monochromatic electromagnetic wave by an inhomogeneity of the velocity of motion of the medium is carried out. The inhomogeneity corresponds to the rotation of a finite portion of the medium with a constant angular velocity under the conditions of spatial homogeneity of the permittivity and the permeability. The case of oblique incidence of the wave is studied. The scattering cross sections for an inhomogeneity having the shape of a cylinder or a sphere of different dimensions are found for different angles of incidence of radiation.     

The Khler-Einstein metric for some Hartogs domains over symmetric domains

We study the complete Kahler-Einstein metric of a Hartogs domainΩbuilt on an irreducible bounded symmetric domainΩ, using a power Nμof the generic norm ofΩ.The generating function of the Kahler-Einstein metric satisfies a complex Monge-Ampere equation with a boundary condition. The domainΩis in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are parameterized by X∈[0,1[. This allows us to reduce the Monge-Ampere equation to an ordinary differential equation with a limit condition. This equation can be explicitly solved for a special valueμ0 ofμ.. We work out the details for the two exceptional symmetric domains. The special valueμ0 seems also to be significant for the properties of other invariant metrics like the Bergman metric; a conjecture is stated, which is proved for the exceptional domains.     

A Comparative Investigation on Model Selection in Independent Factor Analysis

With uncorrelated Gaussian factors extended to mutually independent factors beyond Gaussian, the conventional factor analysis is extended to what is recently called independent factor analysis. Typically, it is called binary factor analysis (BFA) when the factors are binary and called non-Gaussian factor analysis (NFA) when the factors are from real non-Gaussian distributions. A crucial issue in both BFA and NFA is the determination of the number of factors. In the literature of statistics, there are a number of model selection criteria that can be used for this purpose. Also, the Bayesian Ying-Yang (BYY) harmony learning provides a new principle for this purpose. This paper further investigates BYY harmony learning in comparison with existing typical criteria, including Akaik’s information criterion (AIC), the consistent Akaike’s information criterion (CAIC), the Bayesian inference criterion (BIC), and the cross-validation (CV) criterion on selection of the number of factors. This comparative study is made via experiments on the data sets with different sample sizes, data space dimensions, noise variances, and hidden factors numbers. Experiments have shown that for both BFA and NFA, in most cases BIC outperforms AIC, CAIC, and CV while the BYY criterion is either comparable with or better than BIC. In consideration of the fact that the selection by these criteria has to be implemented at the second stage based on a set of candidate models which have to be obtained at the first stage of parameter learning, while BYY harmony learning can provide not only a new class of criteria implemented in a similar way but also a new family of algorithms that perform parameter learning at the first stage with automated model selection, BYY harmony learning is more preferred since computing costs can be saved significantly.     

The Closed Orbits of a Class of Cubic Vector Fields in R3

In this paper, we investigate the isolated closed orbits of two types of cubic vector fields in R₃ by using the idea of central projection transformation, which sets up a bridge connecting the vector field X(x) in R₃ with the planar vector fields. We have proved that the cubic vector field in R₃ can have two isolated closed orbits or one closed orbit on the invariant cone. As an application of this result, we have shown that a class of 3-dimensional cubic system has at least 10 isolated closed orbits located on 5 invariant cones, and another type of 3-dimensional cubic system has at least 26 isolated closed orbits located on 13 invariant cones or 26 invariant cones.