Extensions of perfect GO-spaces and -discrete dense sets

In this paper, we prove that if a perfect GO-space has a -discrete dense set, then has a perfect linearly ordered extension. This answers a problem raised by H. R. Bennett, D. J. Lutzer and S. Purisch. And the result is also a partial answer to an old problem posed by H. R. Bennett and D. J. Lutzer.

     

Banach空间二阶非线性奇异微分方程的解

文中讨论了Banach空间中一类右端具有奇异性的二阶非线性微分方程的边值问题,利用不动点方法,获得了该边值问题解的存在性定理.最后还给出了相应的例子.     

The Conley index over a base

We construct a generalization of the Conley index for flows. The new index preserves information which in the classical case is lost in the process of collapsing the exit set to a point. The new index has most of the properties of the classical index. As examples, we study a flow with a knotted orbit in , and the problem of continuing two periodic orbits which are not homotopic as loops.

     

Arrays for orthogonal designs

A set of square real matrices is said to be amicable if for some permutation σ of the set . An infinite number of arrays which are suitable for any amicable set of eight circulant matrices are introduced. Applications include new classes of orthogonal designs. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 166–173, 2000     

Noisy image segmentation based on nonlinear diffusion equation model

This paper addresses the segmentation problem in noisy image based on nonlinear diffusion equation model and proposes a new adaptive segmentation model based on gray-level image segmentation model. This model also can be extended to the vector value image segmentation. By virtue of the prior information of regions and boundary of image, a framework is established to construct different segmentation models using different probability density functions. A segmentation model exploiting Gauss probability density function is given in this paper. An efficient and unconditional stable algorithm based on locally one-dimensional (LOD) scheme is developed and it is used to segment the gray image and the vector values image. Comparing with existing classical models, the proposed approach gives the best performance.     

Bit-size estimates for triangular sets in positive dimension

We give bit-size estimates for the coefficients appearing in triangular sets describing positive-dimensional algebraic sets defined over Q. These estimates are worst case upper bounds; they depend only on the degree and height of the underlying algebraic sets. We illustrate the use of these results in the context of a modular algorithm.This extends the results by the first and the last author, which were confined to the case of dimension 0. Our strategy is to get back to dimension 0 by evaluation and interpolation techniques. Even though the main tool (height theory) remains the same, new difficulties arise to control the growth of the coefficients during the interpolation process.     

凸分析若干结果探讨

在实线性空间中引进了一类新广义凸集.讨论了它的一些性质,与之相联的Minkowski泛函与分离定理等.我们所得结果是经典凸分析中若干相应结果的推广,改进或等价表达.     

The stable set problem and the lift-and-project ranks of graphs

We study the lift-and-project procedures for solving combinatorial optimization problems, as described by Lovász and Schrijver, in the context of the stable set problem on graphs. We investigate how the procedures' performances change as we apply fundamental graph operations. We show that the odd subdivision of an edge and the subdivision of a star operations (as well as their common generalization, the stretching of a vertex operation) cannot decrease the N₀-, N-, or N₊-rank of the graph. We also provide graph classes (which contain the complete graphs) where these operations do not increase the N₀- or the N-rank. Hence we obtain the ranks for these graphs, and we also present some graph-minor like characterizations for them. Despite these properties we give examples showing that in general most of these operations can increase these ranks. Finally, we provide improved bounds for N₊-ranks of graphs in terms of the number of nodes in the graph and prove that the subdivision of an edge or cloning a vertex can increase the N₊-rank of a graph.Research of these authors was supported in part by a PREA from Ontario, Canada and research grants from NSERC.Mathematics Subject Classification (2000): 0C10, 90C22, 90C27, 47D20     

粒度空间约简及其粗糙集模型研究

针对交可约粒度空间中覆盖、基和粒结构的关系,结合偏序关系的哈斯图,给出一种约简粒度空间的方法.另外,通过限定上、下近似算子的取值范围,重新定义了交可约粒度空间上的粗糙集模型,并讨论了其相关性质.     

Modules with Chain Conditions on Non-essential Submodules

Abstract

We investigate when modules which satisfy the descending (respectively, ascending) chain condition on non-essential submodules are uniform or Artinian (respectively, Noetherian).