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Abstract: This paper describes hybrid mathematical model which couples the mechanics of the mass/spring model to the acoustic wave propagation model for use in generating the acoustic signal emitted by complex structures of paper fibres under strain. A discussion of the coupling method is presented including remarks on the errors encountered intrinsic to the discretisation scheme. The numerical results of a vibrating rubber band and a vibrating paper fibre are compared to their experimental counterparts. The fundamental frequencies of the acoustic signals are compared showing a close agreement between the experimental and numerical results. [Copyright &y& Elsevier]

A quandle is a set with a self-distributive binary operation satisfying a certain condition. Here we construct a monoid (a semi-group with the identity) associated with a quandle. This monoid has a structure of a quandle, which contains the original quandle as a sub-quandle. We call it the enveloping monoidal quandle. The purpose of this paper is to introduce the notion of the enveloping monoidal quandle, and to investigate it. [Copyright &y& Elsevier]

Abstract: The concept of labelled stratified graph (LSG) was introduced in Ţăndăreanu (Knowledge Inform. Syst. 2(4) (2000) 438) in connection with that of knowledge base with output (KBO). The aim of this paper is to present a distinct facet of this concept. We prove several algebraic properties for LSGs and we conclude that a LSG can be used independently of a KBO. In order to realize this aim we define a partial order on the set of all LSGs over a labelled graph G, an equivalence relation on and a partial order on the factor set. The set endowed with becomes a join semilattice with greatest element. Each equivalence class contains an unique LSG, which is named distinguished representative of C. This is the least element of. Particularly we obtain the distinguished representative for the supremum of two classes (DRS) and the greatest distinguished LSG (the least LSG of the greatest element of, denoted GD). Two applications are presented, one for DRS and one for GD. Several opens problems are briefly exposed in the last section. [Copyright &y& Elsevier]