This note revisits a paper from Velan and Florian [Velan and Florian(2002)] dealing with the entropy condition in traffic flow models. It aims to clarify the application of this condition for non-differentiable fundamental diagrams and then to correct some misunderstandings that appear in the above-mentioned paper. Notably, this note clearly exhibits that the non-smoothness of the fundamental d...

This paper presents an algorithm for finding a piecewise linear band which bounds given two-dimensional data. The band is of constant height, and the distance between adjacent slope discontinuities in opposite directions is restricted by two user-specified parameters.

In this paper, an approximate solution of sensitivity matrix of required velocity with final velocity constraint is derived using a piecewise linear gravity assumption. The total flight time is also fixed for the problem. Simulation results show the accuracy of the method. Increasing the midway points for linearization, increases the accuracy of the solution, which this, in turn, depends on the...

In this paper we conjecture that the piecewise linear map f(x) = px1I[0,1/p)(x)+ (sx − s/p)1I[1/p,1](x), p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding. We give a partial proof of the conjecture, in particular for values of p and s such that d− ln(p(1−s)+s) ln s e 6 = d− ln p ln s e.

We extend results from Part I about estimating gradient errors elementwise a posteriori, given there for quadratic and higher elements, to the piecewise linear case. The key to our new result is to consider certain technical estimates for differences in the error, e(x1)− e(x2), rather than for e(x) itself. We also give a posteriori estimators for second derivatives on each element.

This paper presents a method of determining the shape of the surface swept by a tool that follows a 5-axis tool path for machining curved surfaces. The method consists of discretising the tool into pseudo-inserts and identifying imprint points using a modi®ed principle of silhouettes. An imprint point exists for each pseudo-insert and the piecewise linear curve connecting them forms an imprint ...

We complete the program begun by Brin and Squier of characterising conjugacy in Thompson’s group F using the standard action of F as a group of piecewise linear homeomorphisms of the unit interval.

The particle level set technique has been adopted in computer graphics as the method of choice for tracking the surface of simulated liquids. In this poster, we describe a novel technique for modeling such an interface. Our technique is based on a set of oriented particles that provides a piecewise linear approximation to the interface. Using this improved model, we obtain a more accurate repre...

In this paper the problem of minimum cost communication network design is considered where the costs are piecewise linear concave. Several methods are compared: Simulated Annealing method, a heuristic based on the method proposed by Minoux, and a lagrangian method based on lower bounding procedure.