一类非线性代数方程组的并行迭代算法

１．引言考虑非线性代数方程组这里,　　　　　　　　　　　　　　　　　　　　　　　　　　　　为连续的对角映射,二者的导函数均存在,但并不一定连续．这类非线性代数方程组具有丰富的实际背景．譬如,Ｓｔｅｆａｎ问题和许多弱非线性椭圆型偏微分方程,就可归结为（１．１）的数值求解问题．根据方程组（１．１）的特殊结构,并利用矩阵多重分裂思想,文ｔＺ］讨论了一类并行非线性Ｇａｕｓｓ－Ｓｅｉｄｅｌ型迭代算法．这类算法具有很好的数值性质和较高的并行效率·在此基础上,运用松弛加速技术,文［８］进一步研究了一类并行多分…     

Contact Transformations and Local Reducibility of ODE to the Form y‴=0

Orbits of the ODE y=0 in corresponding jet bundles are investigated. Explicit relations for the right-hand side of an arbitrary 3-order ODE necessary and sufficient for the existence of a contact transformation reducing this equation locally to the form y=0 are obtained.     

Radiation inhibition effects in the coherent-state many-atom Jaynes-Cummings model

Summary Radiation inhibition in the many-atom Jaynes-Cummings model being a consequence of cooperative as well as cavity detuning effects is examined. Numerical solutions for the time evolution of the atomic population inversion exhibiting quasi-stationary behaviour are presented. Furthermore, the cooperative energy shift of these quasi-stationary states is numerically computed by using a special projection operator. The authors of this paper have agreed to not receive the proofs for correction.     

A preconditioned conjugate gradient Uzawa-type method for the solution of the stokes problem by mixed Q1–P0 stabilized finite elements

We study the behaviour of a conjugate gradient Uzawa-type method for a stabilized finite element approximation of the Stokes problem. Many variants of the Uzawa algorithm have been described for different finite elements satisfying the well-known Inf-Sup condition of Babu?ka and Brezzi, but it is surprising that developments for unstable ‘low-order’ discretizations with stabilization procedures are still missing. Our paper is presented in this context for the popular (so-called) Q1–P0 element. First we show that a simple stabilization technique for this element permits us to retain the property of a convergence factor bounded independently of the discretization mesh size. The second contribution of this work deals with the construction of a less costly preconditioner taking full advantages of the block diagonal structure of the stabilization matrix. Its efficiency is supported by 2D and. 3D numerical results.     

The numerical solution of the thin film flow surrounding a horizontal cylinder resulting from a vertical cylindrical jet

The numerical solution of the thin film flow surrounding a horizontal cylinder resulting from a single vertical cylindrical jet is obtained. This is effected by transforming the domain of the flow, which contains a free surface, onto a rectangular parallelepiped and using a marching strategy to solve the ensuing parabolic equations. The flow terminates at a finite distance along the cylinder, its position depending on the velocity and mass flux of the jet. A comparison with the usual two-dimensional model in which the jet is replaced by a vertical sheet shows that such a representation is valid provided the overall width of the flow is not too large. In particular, the differences in heat transfer characteristics amount to a few per cent, thus validating the use of the two-dimensional model when applied to heat exchanger tubes. A comparison with the more usual multicolumn case is also considered.     

Two-Dimensional Numerical Simulations of Photon Scanning Tunneling Microscopy: Fourier Modal Method and R-Matrix Algorithm

Numerical simulation of a two-dimensional probe–object system for photon scanning tunneling microscope is presented. The R-matrix propagation algorithm incorporated into the Fourier modal method was used to achieve an extended capability for modeling of a realistic system consisting of both a probe and a sample. The type of the mode guided through the dielectric probe and the coupling of the near-field to fundamental guiding mode in the probe are discussed. The influence of the probe parameters on the near-field images is investigated. Three different probe shapes were simulated in the constant height scanning mode. The transmitted flux intensity through the probe was found to be strongly dependent on the tip shape. The analysis shows a good agreement of the obtained results with the available theoretical works and confirming experimental results. The proposed numerical scheme can find applications for near-field probe characterization and provides an understanding of the degree of perturbation introduced by a probe tip in the experiment.     

带Poisson跳随机微分方程终值与边值问题的适应解

Poisson跳的拟线性倒向随机微分方程x(t) ∫tf(s,x(s),,x(s)) y(s)]dMs =ξ,t∈[0,1],这里M = (W,Q)T,其中W为Wiener过程,Q为补偿Poisson过程.利用区间延拓和 Bihari 不等式证明了在某种弱于Lipschitz条件下方程存在唯一适应解,并给出了解的估计,从而将文章[1]的结论推广到带 Poission 跳的情形.另外,本文还讨论了以下形式的边值问题:dx(t) = f(t,x(t),y(t))dt y(t)dMt,Ax(0) Bx(1) =ξ*,t∈[0,1],并证明了在Lipschitz条件下适应解的存在唯一性.     

Extended Hyperbola Function Method and Its Application to Nonlinear Equations

An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.     

Multiple scattering of gamma rays in water,concrete and sand

The transmitted photon spectra of¹³³Ba,²²Na,¹³⁷Cs,⁵⁴Mn and⁶⁰Co point sources are measured through different thicknesses of water, concrete and sand. The multiple-scatter peaks observed in these materials at 60, 90 and 100 keV energies respectively are found to be independent of incident photon energy and thickness of the medium.