Let G be a group generated by a finite set A. An element g ∈ G is a strict dead end of depth k (with respect to A) if |g| > |ga1| > |ga1a2| > · · · > |ga1a2 · · · ak| for any a1, a2, . . . , ak ∈ A such that the word a1a2 · · ·ak is freely irreducible. (Here |g| is the distance from g to the identity in the Cayley graph of G.) We show that in finitely generated free soluble groups of degree d ≥...

Understanding the operation of filters used to remove particulates from fluids is important in many practical industries. Typically particles are larger than pores filter so a cake layer forms on surface. Here we extend existing models for blocking account deformation material and due applied pressure that drives fluid. These deformations change permeability hence flow. We develop new theory co...

Recently designed cross-layer contention based synchronous MAC protocols like the PRMAC protocol, for wireless sensor networks (WSNs) enable a node to schedule multi-hop transmission of multiple data packets in a cycle. However, these systems accommodate both the request-to-send data process and the confirmation-to-send data process in the same data transmission scheduling window (i.e. data win...

Wireless sensor networks (WSNs) keep attracting the attention of researchers due to the newly emerging areas of application fueled by the development of inexpensive sensors and advanced communication technologies. A large group of applications monitoring of pipelines, roads and bridges, as well as recently evolving IoT applications specifically requires linear topology. Compared to traditional ...