A Technical Note on Weak Shift Equivalence

A note on weak dividing

We study the notion of weak dividing introduced by S. Shelah. In particular we prove that T is stable iff weak dividing is symmetric. In order to study simple theories Shelah originally defined weak dividing in [6] . This notion is overshadowed by that of dividing, as the first author proved that dividing is the right well-behaved notion for simple theories [2],[3],[5],and [4]. However Dolich’s...

A note on equivalence in ranking investments

A note on single-linkage equivalence

We introduce the concept of single-linkage equivalence of edge-weighted graphs, we apply it to characterise maximal spanning trees and “ultrasimilarities”, and we discuss how it relates to the popular single-linkage clustering algorithm.

Strong Shift Equivalence Theory and the Shift Equivalence Problem

This paper discusses strong shift equivalence and counterexamples to the long standing Shift Equivalence Problem in symbolic dynamics. We also discuss how strong shift equivalence theory is closely related to areas of mathematics outside dynamics such as algebraic K-theory, cyclic homology, and topological quantum field theory.

A Note on the Generalized Shift Map

In this short note we have discussed generalized shift map in the symbol space Σ2. Some stronger chaotic properties have been proved. Some special properties are discussed in a different section. In the last section we have also provided few examples.