In this article we prove that an isometric multiple HNN extension of a group satisfying the falsification by fellow traveler property is almost convex. As a corollary, Wise’s example of a CAT(0) non-Hopfian group is almost convex.

We study the second bounded cohomology of an amalgamated free product of groups, and an HNN extension of a group. As an application, we show that a group with infinitely many ends has infinite dimensional second bounded cohomology.

By estimating the subgroup numbers associated with various classes of large groups, we exhibit a number of new phenomena in the theory of subgroup growth. Key-words: subgroup growth, large groups, one-relator groups, HNN-extensions MSC-Index: 20E07

Reduced HNN extensions of von Neumann algebras (as well as C-algebras) will be introduced, and their modular theory, factoriality and ultraproducts will be discussed. In several concrete settings, it will be illustrated how our results can be applied.

We discuss embedding theorems for HNN extensions and clarify the relationship between the concept by Gilbert and that of Yamamura. We employ the automata theoretical technique based on the combinatorial and geometrical properties of Schützenberger graphs.

We prove that the property to be limit aperiodic is preserved by the standard construction with groups like extension, HNN extension and free product. We also construct a non-limit aperiodic G-space.

The computational complexity of the word problem in HNN-extension groups is studied. a fundamental construction combinatorial group theory. It shown that for an ascending H logspace reducible to so-called compressed H. main result paper states hyperbolic with cyclic associated subgroups can be solved polynomial time. This easily extended graphs vertex and edge groups.

This paper considers the problem of applying neural network for logic circuit testing and proposes an efficient method based on hyperneural network (HNN). The HNN uses an energy function that not only considers binary relations but also captures all higher order relations among N neurons. We illustrate the hyperneural concept using two formulations. First, a constraint engery function is define...