单叶调和映射

由于在极小曲面理论中的作用，对调和映射的研究已有较长时间。１９８４年以来，经典解析单叶映射的理论被推广至调和单叶映射，并获得许多结论。这些工作引起人们对它的浓厚兴趣。该文介绍这一课题某些重要成果的概貌，并指出一些尚未解决的问题。它共分六个部分：映射定理；单叶调和函数的数值估计；特殊映射；变分方法；境界性质和在极小曲面中的应用。     

Variational Inclusions for Fuzzy Mappings

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＳｉｄｄｉｑｉａｎｄＡｎｓａｒｉ［４］ｄｅｖｅｌｏｐｅｄｉｔｅｒａｔｉｖｅａｌｇｏｒｉｔｈｍｓｆｏｒｆｉｎｄｉｎｇａｐｐｒｏｘｉｍａｔｅｓｏｌｕｔｉｏｎｔｏｎｅｗｃｌａｓｓｅｓｏｆｑｕａｓｉｖａｒｉａｔｉｏｎａｌｉｎｅｑｕａｌｉｔｉｅｓｉｎＨｉｌｂｅｒｔｓｐａｃｅｓ，ＨａｓｓｏｕｎｉａｎｄＭｏｕｄａｆｉ［１］ｅｘｔｅｎｄｔｈｅｍａｉｎｉｄｅａｓｏｆｐａｐｅｒ［４］ｔｏｍｏｒｅｇｅｎｅｒａｌｃａｓｅｓ，ｗｈｉｃｈｃｏｎｓｉｄｅｒｅｄａｃｌａｓｓｏｆｖａｒｉａｔｉｏｎ…     

三维空间中的有界凸域和拟球

本文证明了三维空间中的有界凸域是拟球，从而也说明了拟共形映照中的黎曼定理在三维空间中的有界凸域上是成立的     

Analysis of grazing bifurcations of quasiperiodic system attractors

This paper presents the first application of the discontinuity-mapping approach to the study of near-grazing bifurcations of originally quasiperiodic, co-dimension-two system attractors. The paper establishes an exact formulation for the discontinuity-mapping methodology under the assumption that a Poincaré section can be found that is everywhere transversal to the grazing attractor. In particular, it is shown that, while a reduced formulation may be employed successfully in the case of co-dimension-one attractors, it fails to capture dynamics in directions transversal to the original quasiperiodic attractor. This shortcoming necessitates the full machinery presented here. The generality of the proposed approach is illustrated through numerical analysis of two nonlinear dynamical systems of dimension three and four.     

在非自然指数下Beltrami方程的L~p可积性

对于n维的 Beltrami方程,存在指数 r_1和r_2,满足1相似文献   

The Berry–Esseen Bound in the Theory of Random Permutations

The convergence rate in the central limit theorem for linear combinations of the cycle lengths of a random permutation is examined. It is shown that, in contrast to the Berry-Esseen theorem, the optimal estimate in terms of the sum of the third absolute moments has the exponent 2/3.     

General KKM Theorem with Applications to Minimax and Variational Inequalities

In this paper, a general version of the KKM theorem is derived by using the concept of generalized KKM mappings introduced by Chang and Zhang. By employing our general KKM theorem, we obtain a general minimax inequality which contains several existing ones as special cases. As applications of our general minimax inequality, we derive an existence result for saddle-point problems under general setting. We also establish several existence results for generalized variation inequalities and generalized quasi-variational inequalities.