On General Volume-Preserving Mechanical Systems via Cohomology

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold(Μ,ω) via the highest Euler-Lagrange cohomology. It is shown that for every volume-preserving fiow there are some 2-forms that play a similar role to the Hamiltonian in the Hamilton mechanics and the ordinary canonical equations with Hamiltonian H are included as a special case with a 2-form Hω/(n - 1).     

The Global Existence of Solutions for a Cross-diffusion System

This paper is concerned with the global existence of solutions for a class of quasilinear cross-diffusion system describing two species competition under self and cross population pressure. By establishing and using more detailed interpolation results between several different Banach spaces, the global existence of solutions are proved when the self and cross diffusion rates for the first species are positive and there is no self or cross-diffusion for the second species.     

Love waves in layered anisotropic media

A modified transfer-matrix method is proposed to describe Love waves in multilayered anisotropic (monoclinic) media. Dispersion relations for media consisting of one and two anisotropic elastic layers in contact with an anisotropic half-space are obtained in closed form. The conditions for Love waves to exist are analysed. Waves with horizontal transverse polarization of the non-canonical type are investigated.     

多元Kantorovich算子L_p范数下的渐近展开

本文给出了高维单纯形上Kantorovich算子在Lp（1＜P＜∞）范数下的高阶渐近展开公式．     

Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm

We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established inthis paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists thediscrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existencein finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodicperturbation. The numerical results are satisfactory.     

Influence of grooves in the electromagnetic transmission of a periodic metallic grating filter

The light transmittance of metal film with periodic slits and grooves structure has been investigated. It was demonstrated that the grooves significantly affect the transmittance of the metal film. The structure excavating two grooves symmetric to the central slit in a cell of a period grating displays a dent in the transmission spectrum comparing with the structure with only one slit in the cell. Deepening the grooves moves the dents to the longer wavelengths in the transmission spectrum. An analytical equation is also provided to approximately locate the dents. The grooves in the grating filter supply the advantage of removing the needless transmission of certain frequency.     

A Class of Non-degenerate Solvable Lie Algebras and Their Derivations

The author constructs a class of indecomposable non-degenerate solvable Lie Algebras corresponding to a Cartan matrix A over the field of complex numbers and we determine all their derivations.     

Continuity in quantitative domains

Based on the notion of an $L$-fuzzy partially ordered set constructed in (An L-fuzzy approach to quantitative domain (I)—generalized ordered set valued in frame and adjunction theory, Fuzzy Systems and Mathematics 14 (2000) 6–7), and by introducing the concepts of an $L$-fuzzy directed set and the join of an $L$-fuzzy set w.r.t. the $L$-fuzzy partial order, $L$-fuzzy domains are defined and the generalized Scott topology on an $L$-fuzzy domain is built. This approach is similar to Flagg's logic approach to quantitative domain theory (A Logical Approach to Quantitative Domain Theory, Elsevier, Amsterdam, 1996, submitted for publication). In addition, the concepts of stratified approximation and a basis for an $L$-fuzzy domain are proposed, and a notion of a continuous $L$-fuzzy domain is developed. It is proved that if $L$ is a completely distributive lattice in which 1 is $\vee$-irreducible and the well below relation is multiplicative, then the stratified interpolation property holds in a continuous $L$-fuzzy domain $(X,e)$, and $\{{\Uparrow }_{a}x\mid 0\ne a⋘1,x\in X\}$ is a base for the generalized Scott topology on $(X,e)$.     

亚乙基硫脲分子键伸缩模式与全耦合模式键极化率的对比及其拉曼激发虚态的相关研究

从拉曼峰强着手,得到了键伸缩模式与全耦合模式两种不同计算条件下,亚乙基硫脲(ethylene thiourea,ETU)分子的键极化率,并比较分析了两种计算结果的异同.研究表明:在键伸缩模式的算法中,仅考虑势能分布中键对称伸缩比重相对较大的部分拉曼峰参与极化率计算,显然忽略了键伸缩与键弯曲间的相互耦合,造成了与弯曲振动耦合较强的部分键伸缩极化率值存在一定误差.因此,此方法虽能使问题简化,但却丢失了一些信息.而全耦合模式算法考虑了所有振动模式(键伸缩与键弯曲)相互影响的情况,能更全面的反映键电荷的分布情况,但却会使问题的求解过程变得复杂.同时,在拉曼激发虚态的相关研究中,两种计算方法却得到几乎一致的键极化率弛豫方式(呈单指数规律衰减)及相同的衰减特征时间.