解强刚性块线代数方程组的两类L-收敛迭代法

对解强刚性块线代数方程组X=(A(?)J)X φ,本文提出了L-收敛的最佳单参数迭代法(L-OOPI)和L-收敛的多参数迭代直接法(L-MPID),并给出了数值例子．数例表明,对于强刚性块线代数方程组,该二迭代法是有效的．     

用带误差项的Ishikawa迭代过程逼近φ-强增生算子的零点

本文使用新的分析技巧研究了一致光滑Ｂａｎａｃｈ空间中φ 强增生算子的零点逼近问题，所得结果改进和扩展了近期许多相应的结果     

Independence of Yang-Mills Equations with Respect to the Invariant Pairing in the Lie Algebra

It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing in the Lie algebra. Moreover, the Hamilton-Cartan equations of these Lagrangians are obtained and proved to be also independent with respect to the pairing. PACS Numbers 2003: 02.20.Qs, 02.20.Sv, 02.20.Tw, 02.40.Ma, 02.40.Vh, 11.10.Ef, 11.15.Kc Mathematics Subject Classification 2000: Primary 70S15, Secondary 58A20, 58E15, 58E30, 70S05, 70S10, 81T13     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.     

Dynamical properties of a stochastic predator-prey model with functional response

A stochastic prey-predator model with functional response is investigated in this paper. A complete threshold analysis of coexistence and extinction is obtained. Moreover, we point out that the stochastic predator-prey model undergoes a stochastic Hopf bifurcation from the viewpoint of numerical simulations. Some numerical simulations are carried out to support our results.     

Submanifolds in Cauchy Riemann Geometry

In this paper I would like to make a report on the results about hypersurfaces in the Heisenberg group and invariant curves and surfaces in CR geometry. The results are contained in the papers [8, 9, 16] and [14]. Besides, I would also report on the results about the strong maximum principle for a class of mean curvature type operators in [10].     

Polariton emission in GaN microcavities

We present a detailed experimental study aimed at demonstrating the polariton nature of the photoluminescence emission in a bulk GaN microcavity grown on (111) silicon. The comparison of the photoluminescence with coincident reflectivity measurements at different temperatures shows an anticrossing behaviour with a Rabi splitting of the order of 35 meV up to room temperature. Relevant confirmations of the mixing between excitons and photons are found in the analysis of the spectral linewidth and of the time resolved kinetics.     

BRST invariance and the conical pendulum

The Hamiltonian formulation of the BRST method for quantizing constrained systems developed recently by Nemeschanskyet al is applied to the well-known problem of the conical pendulum in classical mechanics. The similarity of the system to a gauge theory wherein the two constraints serve as generators of local Abelian gauge transformations is also pointed out. The definition of the physical states of the system as a gauge theory and also as a BRST invariant theory is then discussed in some detail.     

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