一类二阶奇异微分方程正解的存在唯一性

利用上下解方法,不动点理论研究奇异微分方程u" f(t,u)=0,t∈(0,1)在边界条件au(0)-βu'(0)=0,γu(1) δu'(1)=0下C[0,1]正解和C1[0,1]正解的存在性与唯一性.其中非线性项f(t,u)关于u是减的,仅满足较弱的要求.     

VALUE DISTRIBUTION THEORY AND DIOPHANTINE APPROXIMATION

In this paper, we will introduce some problems and results between Diophantine approximation and value distribution theory.     

抛物问题的mortar有限元逼近的瀑布型多重网格法

用瀑布型多重网格法解决椭圆、抛物问题，已有不少研究工作[1-2]，本文对抛物问题的mortar有限元的全离散格式提出瀑布型多重网格法，证明了该方法是最优的，即具有最优精确度和复杂度．     

A theorem on upper-lower solutions for nonlinear elliptic systems and its applications

We report on a result of upper-lower solutions for nonlinear elliptic systems without the assumption of quasi-monotonicity. An application is described involving the existence of positive steady states of a certain interaction system arising in biology and medical sciences.     

Randomized k-server algorithms for growth-rate bounded graphs

The k-server problem is a fundamental online problem where k mobile servers should be scheduled to answer a sequence of requests for points in a metric space as to minimize the total movement cost. While the deterministic competitive ratio is at least k, randomized k-server algorithms have the potential of reaching o(k)-competitive ratios. Prior to this work only few specific cases of this problem were solved. For arbitrary metric spaces, this goal may be approached by using probabilistic metric approximation techniques. This paper gives the first results in this direction, obtaining o(k)-competitive ratio for a natural class of metric spaces, including d-dimensional grids, and wide range of k.     

Totally skew embeddings of manifolds

We study a version of Whitney’s embedding problem in projective geometry: What is the smallest dimension of an affine space that can contain an n-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points? This problem is related to the generalized vector field problem, existence of non-singular bilinear maps, and the immersion problem for real projective spaces. We use these connections and other methods to obtain several specific and general bounds for the desired dimension.     

A difference scheme for solving the Timoshenko beam equations with tip body

In this article, a Timoshenko beam with tip body and boundary damping is considered. A linearized three-level difference scheme of the Timoshenko beam equations on uniform meshes is derived by the method of reduction of order. The unique solvability, unconditional stability and convergence of the difference scheme are proved. The convergence order in maximum norm is of order two in both space and time. A numerical example is presented to demonstrate the theoretical results.     

A new L-curve for ill-posed problems

The truncated singular value decomposition is a popular method for the solution of linear ill-posed problems. The method requires the choice of a truncation index, which affects the quality of the computed approximate solution. This paper proposes that an L-curve, which is determined by how well the given data (right-hand side) can be approximated by a linear combination of the first (few) left singular vectors (or functions), be used as an aid for determining the truncation index.     

Cn中多圆柱体的Riemann-Hilbert边值问题

本文研究了利用Poission核求解C^N（1≤n≤2）中单位多圆柱体上Riemann-Hilbert边值问题．同时，给出了其解的表达式和可解条件，并将原来求解空间从解析函数空间推广到亚纯函数空间．     

A note on optimality conditions for the Euclidean. Multifacility location problem

Thekey problem of the Euclidean multifacility location (EMFL) problem is to decide whether a givendead point is optimal. If it is not optimal, we wish to compute a descent direction. This paper extends the optimality conditions of Calamai and Conn and Overton to the case when the rows of the active constraints matrix are linearly dependent. We show that linear dependence occurs wheneverG, the graph of the coinciding facilities, has a cycle. In this case the key problem is formulated as a linear least squares problem with bounds on the Euclidean norms of certain subvectors.