Variational principles for symmetric bilinear forms

Every compact symmetric bilinear form B on a complex Hilbert space produces, via an antilinear representing operator, a real spectrum consisting of a sequence decreasing to zero. We show that the most natural analog of Courant's minimax principle for B detects only the evenly indexed eigenvalues in this spectrum. We explain this phenomenon, analyze the extremal objects, and apply this general framework to the Friedrichs operator of a planar domain and to Toeplitz operators and their compressions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Faithful compact quantum group actions on connected compact metrizable spaces

We construct faithful actions of quantum permutation groups on connected compact metrizable spaces. This disproves a conjecture of Goswami.     

Small Compact Perturbation of Operators in B∞（Ω）

Abstract： We consider an approximation problem related to strongly irreducible operators, that is, does the direct sum of a strongly irreducible operator in B∞（Ω） and certain operator have a small compact perturbation which is a strongly irreducible operator in B∞（Ω）？ In this paper, we prove that the direct sum of any strongly irreducible operator in B∞（Ω） and certain biquasitriangular operator have small compact perturbations which are strongly irreducible operators in B∞（Ω）.     

集值映射的广义重心选择

给出了广义重心选择的一些结论.对任意r∈R+我们给出了具有紧凸像的映射F的一个选择.并且如果F的像不是凸集我们同样给出了一个选择.     

Contractive projections on Banach algebras

In this paper, we explore the properties of projections of norm one on general Banach algebras, in particular the relation with conditional expectations for algebras which arise in harmonic analysis.     

On subnormal subgroups of linear groups

We describe the subnormal subgroups of 2-dimensional linear groups over local and full rings in which 2 is invertible, as well as the subnormal subgroups of symplectic groups over local rings in which 2 is invertible.     

An intrinsic approach to Lichnerowicz conjecture

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids thenice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.     

《泛函分析》中两个定理的教学与应用

本文讨论《泛函分析》中 Schauder不动点定理和 Arzela-Ascoli定理的教学方法并把它们用于互助生态模型得到两物种共存的一个充分条件 .     

Transient DSC,a Novel and Rapid Method for Assessing Pharmaceutical Powder Compacts

The previously described method involving the use of transient DSC was applied to pharmaceutical powder compacts and to ceramic powder compacts. The samples were prepared by compressing powders of pentaerythritol tetraacetate and two kinds of alumina powder (differing in particle size distribution) up to a pressure of 20 MPa by using a jig. For pentaerythritol tetraacetate, a linear relationship was obtained between the parameter obtained by DSC and the compaction pressure. This revised version was published online in August 2006 with corrections to the Cover Date.     

《数书九章》大衍类算题中的数论命题

《数书九章》是我国著名数学家南宋秦九韶撰写(公元1247年)。青年时他“侍亲中都(临安,今杭州市)因得访习于太史(国家天文历法官员)”。《数书九章》有“大衍总数术”以处理天文历法问题,系统论述同余式解法,这在我国历史上是第一次,在世界数学史上也是创举。 本文用整数论知识来检验《数书九章》中有关解同余式算题(大衍类)题文、术文、草文以及清代学者所作注文的得失,使对我国传统数学在这一领域内的工作有,较系统的认识。