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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]

Abstract: In this paper, we present some sixth-order class of modified Ostrowski’s methods for solving nonlinear equations. Per iteration each class member requires three function and one first derivative evaluations, and is shown to be at least sixth-order convergent. Several numerical examples are given to illustrate the performance of some of the presented methods. [Copyright &y& Elsevier]

Abstract: This paper considers systems that have a measurement that is computed from the post-processing of a short duration image. The measurement can be regarded as the integral of a linear function of the state variables of the system. The input to the system is assumed to be generated with a zero-order hold whose sampling frequency is the same as that of the measurement. The paper presents a discrete-time finite dimensional state variable model for such systems. [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]