猜想M(2k,k+1)=3k-1+[(k-1)/2]的反例

Brualdi与Jung在[1]中研究了一类具有固定线和k的n×n矩阵上的最大跳跃数M(n,k),并提出猜想M(2k, k + 1) = 3k - 1 + [(k-1)/2].本文给出了这一猜想的两个反例．     

Inequalities for the Moments and Distribution of the Ladder Height of a Random Walk

We obtain upper bounds for the tail distribution of the first nonnegative sum of a random walk and for the moments of the overshoot over an arbitrary nonnegative level if the expectation of jumps is positive and close to zero. In addition, we find an estimate for the expectation of the first ladder epoch.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

Operations in A-theory

A construction for Segal operations for K-theory of categories with cofibrations, weak equivalences and a biexact pairing is given and coherence properties of the operations are studied. The model for K-theory, which is used, allows coherence to be studied by means of (symmetric) monoidal functors. In the case of Waldhausen A-theory it is shown how to recover the operations used in Waldhausen (Lecture Notes in Mathematics, Vol. 967, Springer, Berlin, 1982, pp. 390-409) for the A-theory Kahn-Priddy theorem. The total Segal operation for A-theory, which assembles exterior power operations, is shown to carry a natural infinite loop map structure. The basic input is the un-delooped model for K-theory, which has been developed from a construction by Grayson and Gillet for exact categories in Gunnarsson et al. (J. Pure Appl. Algebra 79 (1992) 255), and Grayson's setup for operations in Grayson (K-theory (1989) 247). The relevant material from these sources is recollected followed by observations on equivariant objects and pairings. Grayson's conditions are then translated to the context of categories with cofibrations and weak equivalences. The power operations are shown to be well behaved w.r.t. suspension and are extended to algebraic K-theory of spaces. Staying close with the philosophy of Waldhausen (1982) Waldhausen's maps are found. The Kahn-Priddy theorem follows from splitting the “free part” off the equivariant theory. The treatment of coherence of the total operation in A-theory involves results from Laplaza (Lecture Notes in Mathematics, Vol. 281, Springer, Berlin, 1972, pp. 29-65) and restriction to spherical objects in the source of the operation.     

Equivalences of comodule categories for coalgebras over rings

In this article we defined and studied quasi-finite comodules, the cohom functors for coalgebras over rings. Linear functors between categories of comodules are also investigated and it is proved that good enough linear functors are nothing but a cotensor functor. Our main result of this work characterizes equivalences between comodule categories generalizing the Morita-Takeuchi theory to coalgebras over rings. Morita-Takeuchi contexts in our setting is defined and investigated, a correspondence between strict Morita-Takeuchi contexts and equivalences of comodule categories over the involved coalgebras is obtained. Finally, we proved that for coalgebras over QF-rings Takeuchi's representation of the cohom functor is also valid.     

The push-out region of an immersed manifold

We consider immersions: and construct a subspace of which corresponds to a set of embedded manifolds which are either parallel to f, tubes around f or, in general, partial tubes around f. This space is invariant under the action of the normal holonomy group, We investigate the case where is non-trivial and obtain some results on the number of connected components of . Received 24 March 2000.     

Nielsen realization for 3-manifolds containing two-sided projective planes

For compact irreducible sufficiently large 3-manifolds containing 2-sided projective planes, we consider the following Realization Problem: Given a finite subgroup of the outer automorphism group of the fundamental group, is there a finite group of homeomorphisms, which induces this subgroup? Received: 16 November 1999; in final form: 18 January 2001 / Published online: 8 November 2002