Simplicial normalization in the entire cyclic cohomology of Banach algebras

We show that the entire cyclic cohomology of Banach algebras defined by Connes has the simplicial normalization property. A key tool in the proof is the notion and properties of supertraces on the Cuntz algebraQ A. As an example of further applications of this technique, we give a proof of the homotopy invariance of entire cyclic cohomology.Address after 1st October 1995: Department of Mathematics, University of Exeter, North Park Road, Exeter EX4 4QE, U.K.     

Weak Factorization Systems and Topological Functors

Weak factorization systems, important in homotopy theory, are related to injective objects in comma-categories. Our main result is that full functors and topological functors form a weak factorization system in the category of small categories, and that this is not cofibrantly generated. We also present a weak factorization system on the category of posets which is not cofibrantly generated. No such weak factorization systems were known until recently. This answers an open problem posed by M. Hovey.     

一类海-气振子ENSO模型的同伦分析解法

研究了一个ENSO海-气时滞振子模型.利用同伦分析方法,得到了该模型解的近似展开式,通过与特殊情况下的精确解比较,得到的二级近似解具有较高的精度.     

ON THE EXISTENCE OF ZERO POINTS OF A CONTINUOUS FUNCTION

IPreliminarlesTheee。etOOk totot比OO。stsllCCdCSdO‘lOll‘。山OOqll时1OO/(。)＝。,SS山 SFSSdPoint Theorems[‘’,”],Degree Theory【9,15]．In general these are used when f aPPlies a set ora space on itself．Cm眈inn眈ion Methods can be used to test the existence ofa solution whenf pplies a set or a sp。e on it咖‘－’,”－“l,or aPPlies a set or sP。m another sP。,s。M see here．wrthermore,contlnuulon methods pve us the exlstence ofcurves wb讪 can beused to CalCttlue the Sdutionsl6…     

Stable Homotopy Monomorphisms

It is well known that the concept of monomorphism in a category can be defined using an appropriate pullback diagram. In the homotopy category of TOP pullbacks do not generally exist. This motivated Michael Mather to introduce another notion of homotopy pullback which does exist. The aim of this paper is to investigate the modified notion of homotopy monomorphism obtained by applying the pullback characterization using Mather's homotopy pullback. The main result of Section 1 shows that these modified homotopy monomorphisms are exactly those homotopy monomorphisms (in the usual sense) which are homotopy pullback stable, hence the terminology “stable” homotopy monomorphism. We also link these stable homotopy monomorphisms to monomorphisms and products in the track homotopy category over a fixed space. In Section 2 we answer the question: when is a (weak) fibration also a stable homotopy monomorphism? In the final section it is shown that the class of (weak) fibrations with this additional property coincides with the class of “double” (weak) fibrations. The double (weak) covering homotopy property being introduced here is a stronger version of the (W) CHP in which the final maps of the homotopies involved play the same role as the initial maps.     

K-Theory of Stable Generalized Operator Algebras

It is proved that algebraic and topological K-functors are isomorphic on the category of stable generalized operator algebras which are K _i -regular for all i > 0.     

组合同伦方法在无界域上的收敛性

组合同伦内点法由Feng等提出，是求解有界区域上的非凸数学规划的一种大范围收敛性方法，本文证明此算法适用于某些无界区域上的非凸数学规划问题。     

A brief review of the homotopy analysis method

本文简述同伦分析方法基本思想、最新理论进展及其在流体力学、固体力学、一般力学、量子力学、应用数学、金融等科学和工程领域的应用.同伦分析方法不依赖物理小参数, 适用范围更广,而且提供了一种简单的途径确保级数解收敛, 适用于强非线性问题.同伦分析方法已被成功应用于求解一些具有挑战性的力学问题,并获得一些全新的、 从未见报道的解. 这些成功的应用,证明了同伦分析方法的普遍有效性和原创性.     

一种新的求非线性方程组的数值延拓法

针对迭代过程中的Jacobi奇异问题,本文提出了一种新的数值延拓法.通过构造双参数同伦算子,采用可控条件和适当选取参数的方式克服Jacobi奇异性,并分析了方法的收敛性.最后,通过数值实验对比,验证了方法的可行性和优越性.特别是具有可调控越过Jacobi奇异(点、线、面)的优势,从而也在某种程度上解决了数值延拓法严重依赖于初值的问题.     

Bounded complexes of cotorsion sheaves

We provide a necessary and su?cient condition which ensure that every flat quasi-coherent sheaf has finite cotorsion dimension. Also, we will show that every locally noetherian scheme with a dualizing complex has this requirement.