The concept of HNN-extensions of groups was introduced by Higman, Neumann and Neumann in 1949. HNN-extensions and amalgamated free products have played a crucial role in combinatorial group theory, especially for algorithmic ...

This study discusses the gates of the city of Jerusalem during the Fāṭimid and Saljūq periods through the study of historical sources, contemporary research on this subject and the results of archaeological excavations ...

We prove that the Schutzenberger graph of any element of the HNN-extension of a fnite inverse semigroup S with respect to its standard presentation is a context-free graph, showing that the language L recognized by this ...

The solvability of the word problem for Yamamura’s HNN-extensions [S; A1, A2; ϕ] has been proved in some particular cases. However, we show that, contrary to the group case, the word problem for [S; A1A2; ϕ] is undecidable ...

Crop yield in low-rainfall environments is a complex trait under multigenic control that shows significant genotype×environment (G×E) interaction. One way to understand and track this trait is to link physiological studies ...

We study D- and c-optimal designs for dose-finding with opposing failure functions. In particular, we study the contingent response models of Li, Durham and Flournoy (1995). In the contingent response model, there are two ...

Background: There are a number of unresolved issues in the design of experiments in greenhouses. They include whether statistical designs should be used and, if so, which designs should be used. Also, are there thigmomorphogenic ...

We generalize results in the literature to obtain a general family contingent response models. These models have ternary outcomes constructed from two Bernouli outcomes, where one outcome is only observed if the other ...