抛物问题的拉格朗日乘子区域分解法

１．引言 近年来,一类新的非重叠区域分解方法一非匹配网格区域分解法,日益引起人们的广泛兴趣,并已成为当今区域分解方法研究的热门课题。这类区域分解方法的特点是：相邻子区域在公共边（或面）上的结点可以不重合,从而能解决许多传统区域分解方法不便解决的问题（如变动网格问题）．目前主要有两类方法来处理这种区域分解的强非协调性：Ｍｏｒｔａｒ无法（见［１－２］和［９－１０］）和拉格朗日乘子法（见［５］,［８］,［１１］和［１２］）．拉格朗日乘子法比Ｍｏｒｔａｒ无法有明显的优点：（１）界面变量（即拉格朗日乘子）…     

几族3-优图

一个图 G中含有的三个结点的导出连通子图的个数 S3( G)在网络可靠性中起着重要作用 .在同点数同边数图类中具有最大 S3( G)的图称为 3-优图 ,它所代表的网络是点故障概率接近 1时的最可靠网络 .本文在已有的结果上进一步证明补图为 a K3∪ b K2 ∪ K1和 a K3-x的图分别是各自图类中唯一的 3-优图 ;补图为 a K3∪ ( b-1 ) K2 ∪ 2 K1和 ( a-1 ) K3∪ b K2 ∪ P3的图是该图类中仅有的两个 3-优图 .     

同调函子的一个应用

本文利用同调函子给出了交换的 Noether环上单模的投射性与内射性是等价的一个简单证明 ,同时推广了文 [1]的一些结论     

关于压缩算子的不变子空间

证明关于压缩算子的如下不变子空间定理：如果T是Hilbert空间H上的压缩算子,且集合Z’={λ∈D;存在z∈H,使得‖z‖=1,且‖（λ-T）z‖＜1/3(1-‖λ‖}是开单位圆D的控制集,那么T有非平凡的不变子空间,这个定理包含了S.Brown,B.Chevreau,C.fPearcy和B.Beauzamy的两个重要结果作为特殊情况,特别是,为个定理包含了S.Brown等人的Hilbert空间上的每个具有厚谱的压缩算子都有平凡的不变子空间这个重要结果作为特殊情况。     

分配P-代数的核理想与余核滤子

本文的主要结果是给出了分配P-代数中一个理想成为核理想的充要条件,同时提出了余核滤子的概念,研究了核理想与余核滤子之间的某些内在联系.     

Interaction of solitary waves in magnetized warm dusty plasmas with dust charging effects

In consideration of adiabatic dust charge variation, the combined effect of the external magnetized field and the dust temperature on head-on collision of the three-dimensional dust acoustic solitary waves is investigated. By using the extended Poincar\'e--Lighthill--Kuo method, the phase shifts and the trajectories of two solitons after the collision are obtained. The effects of the magnitude and the obliqueness of the external magnetic field and the dust temperature on the solitary wave collisions are discussed in detail.     

Waveguides induced by grey screening solitons

We investigate the properties of waveguides induced by one-dimensional grey screening solitons in biased photorefractive crystals. The results show that waveguides induced by grey screening solitons are always of single mode for all intensity ratios, i.e. the ratios between the peak intensity of the soliton and the dark irradiance. Our analysis indicates that the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton increase monotonically with intensity ratio increasing. On the other hand, when the soliton greyness increases, the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton decrease monotonically. Relevant examples are provided where photorefractive crystal is of the strontium barium niobate type.     

Evolution and stability of spatial solitons in a photorefractive two-wave mixing system

The dynamical evolution and stability of bright dissipative holographic solitons in biased photorefractive materials in which the self-trapping beam obtains a gain from the pump beam via two-wave mixing has been investigated numerically. Results show that these solitons are stable relative to small perturbations. Adjusting some system parameters, such as the bias field and the angle between beams, can easily control the generation of such solitons. Potential applications in optical switches or repeaters are discussed.     

Two-dimensional relativistic electromagnetic dromion-like soliton in a cold transparent plasma

By using a standard multiple scale method, a Davey--Stewartson (DS) equation has been derived and also applied to a multi-dimensional analytical investigation on the interaction of an ultra-intense laser pulse with a cold unmagnetized transparent electron-ion plasma. The regions of instability are found by considering the modulation instability of a plane wave solution of the DS equation. The DS equation is just of the Davey--Stewartson 1 (DS1) type and admits a dromion solution, i.e. a two-dimensional (2D) dromion soliton decaying exponentially in all spatial directions. A 2D relativistic electromagnetic dromion-like soliton (2D REDLS) is derived for a vector potential.     

Phonon spectrum and related thermodynamic properties of microcrack in bcc-Fe

The phonon spectrum and the related thermodynamic properties of microcracks in bcc-Fe are studied with the recursion method by using the Finnis--Sinclair (F--S) N-body potential. The initial configuration of the microcracks is established from an anisotropic linear elastic solution and relaxed to an equilibrium by molecular dynamics method. It is shown that the local vibrational density of states of the atoms near a crack tip is considerably different from the bulk phonon spectrum, which is closely associated with the local stress field around the crack tip; meanwhile, the local vibrational energies of atoms near the crack tip are higher than those of atoms in a perfect crystal. These results imply that the crack tip zone is in a complex stress state and closely related to the structure evolution of cracks. It is also found that the phonon excitation is a kind of local effect induced by microcracks. In addition, the microcrack system has a higher vibrational entropy, which reflects the character of phonon spectrum related to the stress field induced by cracks.