解含非线性源项的变分不等式问题的非重叠区域分解法

１．引言 近十几年来,变分不等式区域分解算法方面的研究取得了很多成果．特别是重叠型区域分解法方面的研究更是硕果累累,读者可参阅［１－８］等文献．而非重叠型区域分解法方面的研究目前相关结论不多,只有文献［９］针对线性算子单障碍问题提出了一类多子域非重叠区域分解算法（该方法的基本思想来自于工程中早已运用的子结构法）,证明了它的收敛性,并给出了收敛速度分析． 本文将针对含非线性源项的变分不等式问题提出一类多子域非重叠区域分解算法,并给出其收敛性和收敛速度分析． ２．问题及其有限元逼近 设ｎ为ＲＺ中有界凸多…     

On Exponentially Shaped Josephson Junctions

The paper deals with a third order semilinear equation which characterizes exponentially shaped Josephson junctions in superconductivity. The initial-boundary problem with Dirichlet conditions is analyzed. When the source term F is a linear function, the problem is explicitly solved by means of a Fourier series with properties of rapid convergence. When F is nonlinear, appropriate estimates of this series allow to deduce a priori estimates, continuous dependence and asymptotic behaviour of the solution.     

On the decay process of turbulence at large Reynolds and Peclet numbers

When fluctuating temperature field is considered to be super imposed on a general field of eddy turbulence, the early period decay phenomena in regard to velocity, temperature and velocity-temperature are guided by three dynamical equations that are obtained here in a straightforward manner. The equations so obtained are simplified for the case of homogeneous turbulence and subsequently for the case of homogeneous and isotropic turbulence.     

Oscillation of a Punch Moving on the Free Surface of an Elastic Half Space

The contact problem concerning oscillation of a circular rigid punch, moving uniformly at sub-Rayleigh speed along the surface of an elastic half space, is investigated using a three-dimensional formulation. Slow motion of the punch is considered, which implies that the characteristic time for the external loading is much larger than the time interval necessary for shear waves to propagate across the punch. An asymptotic solution for the vertical oscillation of the punch is given. It is shown that the vertical displacement of the punch can approximately be described by the equation of dynamics for a system of one degree of freedom with viscous friction. The dependence of the coefficients for effective viscosity and stiffness, occurring in this equation, on the speed of the punch and Poisson ratio of the half space, is investigated. The solution for the non-stationary problem concerning a suddenly applied moving point load is also obtained, correcting and extending the result known so far. Mathematics Subject Classifications (2000) 74H10, 74J05, 74M15.     

Viscous lifting and drainage of a conducting fluid in the presence of a transverse magnetic field

A theoretical investigation of the effects of a transverse magnetic field on the combined problem of viscous lifting and drainage of a conducting fluid on a plate is presented. The effects of inertia and transverse magnetic field on the liquid film thickness is studied for two cases namely a plate withdrawn with a constant velocity and one withdrawn with a constant acceleration. The expressions for the flow rate and the free surface profiles are obtained for the above two cases. It is found that the free surface profiles are convex in nature as in the non-magnetic case thus showing that the inertia does not effect the general pattern of flow, and the effect of the magnetic field is to retard both the lifting and drainage of the fluid.     

具有一般学习效应的单机排序问题

在具有学习效应的环境下,由于机器重复加工相同或相似的工件,因此以后加工的工件的加工时间变小.本文研究新的更一般的学习效应:Dejong学习效应.我们证明单机最大完工时间问题,总完工时间问题和两类多目标问题是多项式时间可解的.     

Ap(φ)上Toeplitz算子的半换位子

本文给出加权Bergman空间A^p(φ)上具有界调和符号的Toeplitz算子的半换位子为零或为紧算子的一些充要条件.     

EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION

In this paper, the boundary value problems of p-Laplacian functional differential equation are studied. By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.     

关于一些级数取整值问题的注记

利用Pell方程的理论,讨论了与广义Lucas数有关的一些级数的取整值问题.在一定条件下,解决了一些级数的取整值问题.     

树的第二个最大特征值

本文得到了边独立数为n且阶为2n+2的树的第二个最大特征值的精确上界,且给出了达到上界的所有的极树.