The p-chain Spectral Sequence

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to compute algebraic K- and L-groups of group rings and topological K-groups of reduced group C*-algebras.     

Modules with the Direct Summand Sum Property

The present work gives some characterizations of R-modules with the direct summand sum property (in short DSSP), that is of those R-modules for which the sum of any two direct summands, so the submodule generated by their union, is a direct summand, too. General results and results concerning certain classes of R-modules (injective or projective) with this property, over several rings, are presented.     

Spontaneous Surgery on the Borromean Rings

We study the cone-manifolds whose singular sets are obtained by orbifold and spontaneous surgeries on components of the Borromean rings. We establish existence of geometric structures on these manifolds. For manifolds with hyperbolic structure we obtain an integral representation for volumes.     

A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

We construct a new family of cyclic difference sets with parameters ((3 ^d – 1)/2, (3 ^{d – 1} – 1)/2, (3 ^{d – 2} – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.     

The p-Blocks of the Mackey Algebra

Let p be a prime number. This paper describes the primitive idempotents and prime spectrum of the crossed Burnside algebra of a finite group over a p-local ring. The main application is a formula for the block idempotents of the p-local Mackey algebra of the group, in terms of the corresponding bloks of the group algebra.     

非线性差分方程组多正解的存在性

本文应用不动点指数理论证明了一个非线性差分方程组多正解的存在性.     

关于AP-内射环的一个注记

本文的主要目的是讨论AP-内射环中的两个问题:(1)环R是正则的当且仅当R是左AP-内射的左PP-环;(2)如果R是左AP-内射环,那么R是内射环当且仅当R是弱内射环.因此我们推广了内射环的一些结果,与此同时我们还取得了一些新的结果.     

An example in holomorphic fixed point theory

If is the open unit ball in the Cartesian product furnished with the -norm , where and , then a holomorphic self-mapping of has a fixed point if and only if for some

     

Fixed point of multivalued mapping in uniform spaces

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.     

On the solution of Falkner-Skan equations

New existence and uniqueness proofs are given for the solutions of the equations governing the self-similar compressible boundary layer (Falkner-Skan equations). The properties of the solutions are studied and some bounds on important quantities are concluded. The paper is restricted to favourable pressure gradients and to wall cooling.