Abstract In this paper we consider iterated function systems (IFS) on the real line consisting of continuous piecewise linear functions. We assume some bounds contraction ratios functions, but do not any separation condition. Moreover, require that functions IFS are injective, their derivatives separated from zero. prove if fix all slopes perturb other parameters, then for parameters outside an...

This work is part of a syndetic approach to the evaluation of the usability of interaction devices that takes into account the cognitive resources needed to use a device to perform particular tasks. In the syndetic approach both a cognitive model and a model of system behaviour are speciied and brought together within a single framework in order to investigate their relations. The ICS model is ...

In this paper, two kinds of vibrations are considered for a composite Timoshenko rotor: longitudinal-torsional vibration and two plane transverse one. The kinetic and potential energies and virtual work due to the gyroscopic effects are calculated and the set of six governing equations and boundary conditions are derived using Hamilton principle. Differential quadrature method (DQM) is used as ...

In this paper, we propose a new representation of numeric functions using a piecewise arithmetic expression. To represent a numeric function compactly, we partition the domain of the function into uniform segments, and transform the sub-function in each segment into an arithmetic spectrum. From this arithmetic spectrum, we derive an arithmetic expression, and obtain a piecewise arithmetic expre...

Research on Helly-type theorems in combinatorial convex geometry has produced volumetric versions of Helly's theorem using witness sets and quantitative extensions Doignon's theorem. This paper combines these philosophies presents for the integer lattice with axis-parallel boxes as sets. Our main result shows that, while Helly numbers grow polynomially each fixed dimension, their variants are u...