This note is intended as an introduction to two previous works respectively by Dahmani, Guirardel, Osin, and Cantat, Lamy. We give proofs of a Small Cancellation Theorem for groups acting on simplicial tree. discuss the application group plane polynomial automorphisms over any ground field.

Reaction wheels (RWs) used for attitude control of space vehicle systems usually encounter with undesired wide band noises. These noises which significantly affect the performance of regulator controller must tune the review or review rate of RWs. According to wide frequency band of noises in RWs the common approaches of noise cancellation cannot conveniently reduce the effects of the noise. Th...

Shephard groups are common extensions of Artin and Coxeter groups. They appear, for example, in algebraic study of manifolds. An infinite family of Shephard groups which are not Artin or Coxeter groups is considered. Using techniques form small cancellation theory we show that the groups in this family are bi-automatic.

The conditions for the cancellation of all gauge, gravitational, and mixed anomalies of N = 1 supersymmetric models in six dimensions are reviewed and illustrated by a number of examples. Of particular interest are models that cannot be realized perturbatively in string theory. An example of this type, which we verify satisfies the anomaly cancellation conditions, is the K3 compactification of ...

with the property that for any pair r, s of elements of R either r = s or there is very little free cancellation in forming the product rs. The classical example of such a group is the fundamental group of a closed orientable 2-manifold of genus k. The study of this group has given rise both to the theory of one-relator groups, initiated by Magnus ([3]), and to the theory of small cancellation ...