剖析马氏链平稳分布的讲解——谈《应用随机过程》教学

通过平稳分布在Google搜索技术中的应用角度讲解马氏链的平稳分布的概念,并在此基础上对应用随机过程的教学做了粗浅的探讨.     

Approximately unital operator systems

The main theme of this paper is to consider a notion of 'approximately unital operator systems' including both C*-algebras and unital operator systems.The goals are to prove a version of the Choi-Effros theorem for these systems,to introduce a functorial process for forming an approximately unital operator systems from a given matrix ordered vector space with a proper approximate order unit,to study second duals of these objects and to prove that a C*-algebra can be characterized as an approximately unital ...     

特征值问题的预变换方法(I): 杨辉三角阵变换与二阶PDE 特征多项式

本文提出一类求解特征值问题的下三角预变换方法, 目标是通过相似变换后矩阵下三角元素平方和明显减少、且变换后的特征值及其特征向量较易求解, 使变换后的对角线可作为全体特征值很好的一组初值, 其作用如同对于解方程组找到好的预条件子, 加速迭代收敛. 以二阶PDE 数值计算为例,对于以Laplace 方程为代表的特征波向量组及正交多项式组有广泛的应用前景.
杨辉三角是我国古代数学家的一项重要成就. 本文引入杨辉三角矩阵作为预变换子, 给出一般矩阵用杨辉三角矩阵作为左、右预变换子时变为上三角矩阵的充要条件, 给出了元素为行指标二次多项式的两个矩阵类(三对角线阵与五对角线阵) 中特征值何时保持二次多项式的充要条件, 并应用于构造新的二元PDE 正交多项式.     

非Lipschitz条件Hilbert空间上扩散过程的短时间大偏差原理

Under the non-Lipschitzian condition, a small time large deviation principle of diffusion processes on Hilbert spaces is established. The operator theory and Gronwall inequality play an important role.     

交换环上的严格上三角代数上的双导子

Let Nn（R）be the algebra consisting of all strictly upper triangular n × n matrices over a commutative ring R with the identity.An R-bilinear map φ ：Nn（R）×Nn（R）→ Nn（R）is called a biderivation if it is a derivation with respect to both arguments.In this paper,we define the notions of central biderivation and extremal biderivation of Nn（R）,and prove that any biderivation of Nn（R）can be decomposed as a sum of an inner biderivation,central biderivation and extremal biderivation for n ≥ 5.     

Incomplete active polarimetry: Measurement of the block-diagonal scattering matrix

The problem of measurement of block-diagonal scattering matrix as being part of the so-called incomplete or partial Mueller polarimetry is addressed. It has been shown that non-zero elements of the scattering matrix with block-diagonal structure can be measured using only two elliptical polarizations of input light. Optimal pairs of these polarizations are derived. Utilization of the optimal input polarizations results in halving measurement time and decreasing measurement errors by 30%.     

A novel terahertz wave reflective polarizer for THz communication

We design terahertz wave reflective polarizer that operates over a wide terahertz wavelength range and is based on a periodic bilayer structure. The structure is characterized by transfer matrix calculations. Results of simulations show that the mirror is highly reflecting for incidence angle θ ≤ 60°and TE as well as TM polarization in the wavelength range between 541.6 μm and 574.2 μm (i.e. frequency band between 522.5GHZ and 533.9 GHZ). As the incidence angle increases this reflection band blueshifts for both TM and TE polarizations.     

Two-dimensional shift-orthogonal random-interleaving phase-code multiplexing for holographic data storage

A novel phase encoding technology for phase-code multiplexing in holographic data storage (HDS) system called two-dimensional shift-orthogonal random-interleaving (2-D SORI) phase encoding is proposed. Compared with the traditional one-dimensional orthogonal phase-code multiplexing methods, the 2-D method is less sensitive to the variations of the diffraction amplitude and to the phase error of the phase mask. Phase masks for the 2-D SORI phase-code multiplexing can be generated by shifting an elaborately designed phase plate at a certain step, which can avoid the use of a high-cost phase spatial light modulator for the generation of multiple orthogonal phase masks. The cross-talk arising from the systematic phase defects of the static phase modulator is eliminated by the shift operation of the phase plate. Phase codes are interleaved under a predetermined random mapping rule to prevent unauthorized users from accessing the data and eliminate the Bragg degeneration cross-talk. A 2-D SORI phase plate with the size of 5.12 mm × 10.24 mm is designed and fabricated, from which 128 orthogonal phase patterns are generated. The feasibility of the 2-D SORI phase-code multiplexing method for HDS is experimentally demonstrated.     

大模场啁啾光纤光栅的光谱特性

 将一种矩阵算法拓展应用于数值求解多模耦合模微分方程, 并使用该矩阵算法对大模场啁啾光纤光栅的光谱特性进行了理论研究。结果表明, 大模场多模光纤光栅因模式的自耦合和互耦合而使反射谱存在多个反射峰, 这与单模光纤光栅的反射谱不同。由于光栅周期存在啁啾, 大模场光纤光栅的反射峰分裂, 且峰值反射率减小。使用高斯切趾函数可使反射峰分裂在一定程度上得到改善。     

Er3+:Yb3+共掺固体激光器的谐振腔设计及实验研究

考虑激光棒的热透镜效应对有源平平腔、平凹腔进行了数值计算,分析了谐振腔内激光光斑及腔体的稳定性.实验中以Er3+:Yb3+共掺磷酸盐玻璃为工作介质,成功地实现了平凹腔在常温下连续输出TEM00模的1.54μm激光,最大输出功率为21.5mW,光光转换效率达到了0.7%.