A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K.C . O'Meara, and the authors. To clarify some aspects of these new developments, we introduce and study the notion of almost isomorphism between finitely generated projective mod...

The asymptotic properties of random regular graphs are objects of extensive study in mathematics and physics. In this paper we argue, using the theory of spin glasses in physics, that in random regular graphs the maximum cut size asymptotically equals the number of edges in the graph minus the minimum bisection size. Maximum cut and minimal bisection are two famous NP-complete problems with no ...

Asymptotic properties of random regular graphs are object of extensive study in mathematics. In this note we argue, based on theory of spin glasses, that in random regular graphs the maximum cut size asymptotically equals the number of edges in the graph minus the minimum bisection size. Maximum cut and minimal bisection are two famous NP-complete problems with no known general relation between...

There is a close relation between comprehensive Gröbner bases and non-parametric Gröbner bases over commutative von Neumann regular rings. By this relation, Gröbner bases over a commutative von Neumann regular ring can be viewed as an alternative to comprehensive Gröbner bases. (Therefore, this Gröbner basis is called an “alternative comprehensive Gröbner basis (ACGB)”.) In the first part of th...

The automatic extraction of biographical information from business news is a complex task. This approach deals with the characterization of the so called biographical relations by means of local grammars. In order to provide a well-founded proceeding, it is necessary to give a complete and accurate definition of the notion “relation” seen here as a social relationship between human beings or ex...

Discourse analysis may seek to characterize not only the overall composition of a given text or corpora but also the dynamic patterns within the data. Patterns of interest may occur at multiple levels, from character to sentence to corpus. Researchers may be interested in the way that sentence structures recur between participants or how affect words cluster in a single text. Recurrence analyse...

This paper adresses the problem of eecient mappings of nested loops, and more generally of systems of aane recurrence equations, into regular arrays. The presented technique is based on the transformation of an initial systolic mapping. By studying the processor element (PE) activity, a nearly space-optimal mapping is designed by serializing the computations of several initial PEs into a single...