Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call itM-homotopy), discuss its properties and applications. They prove that the weak graphmap homotopy equivalence between graphs coincides with the graph homotopy equivalencedefined by Yau et al in 2001. The difference between them is that the weak graph maphomotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages overthe graph homotopy transformation. As its applications, they investigate the mappingclass group of a graph and the 1-order MP-homotopy group of a pointed simple graph.Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph isinvariant up to the weak graph map homotopy equivalence.     

横向载荷作用下轴向运动梁的屈曲失稳以及非线性振动特性

梁的轴向运动会诱发其产生横向振动并可能导致屈曲失稳,对结构的安全性和可靠性产生重大的影响。本文重点研究了横向载荷作用下轴向运动梁的屈曲失稳及横向非线性振动特性。基于Hamilton变分原理,建立了横向载荷作用下轴向运动梁的动力学方程,获得了梁的后屈曲构型。使用截断Galerkin法,将控制方程改写成Duffing方程的形式。用同伦分析方法确定载荷作用下轴向运动梁的非线性受迫振动的封闭形式的表达式。结果表明,后屈曲构型对轴向速度和初始轴向应力有明显的依赖性。通过同伦分析法得出非线性基频的显式表达式,获得了初始轴向力会影响非线性频率随初始振幅和轴向速度的线性关系。另外,轴向外激励的方向也会改变系统固有频率。     

TheK-theory of AF embeddings of the rational rotation algebras

Our main result is the construction of an embedding ofC(T²) into an approximately finite-dimensionalC ^*-algebra which induces an injection onK ₀(C(T²)). The existence of this embedding implies that Cech cohomology cannot be extended to a stable, continuous homology theory forC ^*-algebras which admits a well-behaved Chern character. Homotopy properties ofC ^*-algebras are also considered. For example, we show that the second homotopy functor forC ^*-algebras is discontinuous. Similar embeddings are constructed for all the rational rotation algebras, with the consequence that none of the rational rotation algebras satisfies the homotopy property called semiprojectivity.     

Topological,affine and isometric actions on flat riemannian manifolds II

Explicit examples of finite subgroups of the group of homotopy classes of self-homotopy equivalences of some flat Riemannian manifolds which cannot be lifted to effective actions are given. It is also shown that no finite subgroups of the kernel of π₀(Homeo(M))→Out π₁(M) can be lifted back to Homeo(M), for a large class of flat manifolds M. Some results of an earlier paper by the authors are refined and related to recent work of R. Schoen and S.T. Yau.     

A note on asymptotic homomorphisms

Using the notion of asymptotic homomorphism due to Connes and Higson we construct bivariant homology-cohomology theories for separableC*-algebras, which satisfy general excision axioms and are nonperiodic.     

模范畴与余模范畴之间的等价

本文研究了环上模范畴与余环上余模范畴.运用可裂叉与余可分余环的性质,得到了以上两个范畴等价的一些充分条件,从而推广了文献[6]中的一些结果.

Abstract：

In this article,we consider the categories of modules over rings and categories of comodules over corings.By properties of split forks and coseparable corings,we get some sufficient conditions for the equivalence between above two categories.As a consequence,we generalize some results in[6].     

具有不同渗透的涨缩管道内微极性流动的同伦分析解

分析了壁面具有不同渗透的涨缩管道内微极性流体的流动．对于壁面的胀缩,考虑常系数和时间函数的膨胀率两种情况．对于第1种情况,应用同伦分析方法得到该问题的速度和微旋转角度的表达式．并且画图分析了各个不同参数,特别是膨胀系数和不同的渗透率对流体的动力特征的影响．可以得到第1个重要的结论：壁面的膨胀率和不同的渗透对流体的动力特征有重要的影响．根据Xu的模型,考虑了第2种也是更具有一般性的情况,假设壁面的膨胀率随时间的变化而变化．在这样的假设下,控制方程被转化成非线性偏微分方程,并且同样也可以应用HAM方法进行求解．应用代数和指数的模型来描述膨胀率从初始状态到最终状态的演变过程．然而,结果表明包含有时间的解很快地趋向于稳态的解．这样可以得到第2个重要的结论,时间在壁面的膨胀收缩中扮演着次要的角色,可以忽略不计．