广义鞍点问题的改进的类SOR算法

针对广义鞍点问题,本文提出了一个改进的类逐次超松弛迭代算法,在较弱的条件下,分析了算法的收敛性及线性收敛率.新算法的每步计算量与已有的算法类似,都是需要（近似）求解线性方程组,但新算法有更好的灵活度通过合适地选取参数矩阵,每一步子问题可以容易地求解,甚至可以有闭式解（closed-form solution）.数值实验结果显示了新算法的有效性.     

稳恒扩展裂纹尖端的弹粘塑性场

采用弹粘塑性力学模型代替通常的弹塑性模型，对于I型和Ⅱ型问题，分别求得了不可压缩材料中平面应变动态扩展裂纹尖端的指数奇异性场和对数奇异性场，消除了弹塑性解中存在的塑性激波。通过数值计算，分别求得了两种奇异属性的分界线，建立起统一的裂纹尖端奇异性场。     

一种变厚度的精化壳体理论及其应用

在Reddy型高阶壳体理论的基础上，采用沿壳体厚度方向的剪切应变呈抛物线分布并且能够满足在壳体的上下表面为零的假设，发展出了一种适合于对变厚度壳体进行非线性分析的方法。该方法利用Ritz原理得到问题的控制方程。通过对一种典型的变厚度壳体结构（子午线轮胎）的结构分析，该方法的计算结果与商用有限元软件的三维分析结果能够很好的吻合。表明了该方法的适用性和有效性。     

Banach空间二阶周期边值问题解的存在性

利用一些比较结果，讨论了Banach空间中二阶周期边值问题解的存在性，获得了若干解的存在性与唯一性结果。     

材料物性参数识别的梯度正则化方法

本文对梯度正则化方法（Ｇｒａｄｉｅｎｔ－Ｒｅｇｕｌａｒｉｚａｔｉｏｎ Ｍｅｔｈｏｄ）作了进一步的研究,给出一种建立了梯度正则化迭代算法和选择正参数的简明实用方法。文中椭圆算子方程参数识别算例不仅说明了ＧＲ法具有广泛的适应性和一定的抗噪声能力,而且收敛速度较快,具有较大的收敛范围。     

关于水气界面处的气体传输

水气界面处的气体传输问题由于其对于地球大气中温室效应气体收支的重要意义,近年来受到广泛的关注．综述国际上在水气界面处传质研究的新进展,在简评各种基本的传质模型基础上,着重介绍在剪切水气界面附近湍流相干结构及其与气体传输的关系方面的一些新发现、新观点．对于实际海气界面气体传输的若干机制进行了评述．为实际估算海气界面处气体传输速度的目的,建议了一种综合考虑剪切与波破碎两种机制的气体传输复合计算方法,得到与实测较满意的符合．      

Robust dropping criteria for F-norm minimization based sparse approximate inverse preconditioning

Drop tolerance criteria play a central role in Sparse Approximate Inverse preconditioning. Such criteria have received, however, little attention and have been treated heuristically in the following manner: If the size of an entry is below some empirically small positive quantity, then it is set to zero. The meaning of “small” is vague and has not been considered rigorously. It has not been clear how drop tolerances affect the quality and effectiveness of a preconditioner M. In this paper, we focus on the adaptive Power Sparse Approximate Inverse algorithm and establish a mathematical theory on robust selection criteria for drop tolerances. Using the theory, we derive an adaptive dropping criterion that is used to drop entries of small magnitude dynamically during the setup process of M. The proposed criterion enables us to make M both as sparse as possible as well as to be of comparable quality to the potentially denser matrix which is obtained without dropping. As a byproduct, the theory applies to static F-norm minimization based preconditioning procedures, and a similar dropping criterion is given that can be used to sparsify a matrix after it has been computed by a static sparse approximate inverse procedure. In contrast to the adaptive procedure, dropping in the static procedure does not reduce the setup time of the matrix but makes the application of the sparser M for Krylov iterations cheaper. Numerical experiments reported confirm the theory and illustrate the robustness and effectiveness of the dropping criteria.     

Coexistence states of a three-species cooperating model with diffusion

In this article, a Lotka--Volterra three-species time-periodic mutualism model with diffusion is investigated. Some sufficient conditions for the existence and estimates of coexistence states are established. Meanwhile, with the assistance of functional analysis methods, some sufficient or necessary results for the existence of positive steady state of the model are presented. Our approach to the discussion is mainly based on the skill of sub- and super-solutions for a general reaction--diffusion system.