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.

Characterizations of the sets with mixed integer programming (MIP) formulations using only rational linear inequalities (rational MILP representable) and those with formulations that use arbitrary closed convex constraints (MICP representable) were given by Jeroslow and Lowe (1984), and Lubin, Zadik and Vielma (2017). The latter also showed that even MICP representable subsets of the natural nu...

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.

We introduce an extended representation of time series that allows fast, accurate classification and clustering in addition to the ability to explore time series data in a relevance feedback framework. The representation consists of piecewise linear segments to represent shape and a weight vector that contains the relative importance of each individual linear segment. In the classification cont...

This paper deals with the adaptation to fuzzy goal programming of the most used methods to formulate, as a linear programming problem, a classic goal programming problem with piecewise linear penalty functions. Up to now, the literature has been only dealing with the adaptation of the Charnes and Cooper’s method. In this paper we show that the mentioned adaptations are not completely correct. W...

This paper studies open-loop stabilization problem for bimodal systems with continuous vector field. It is based on the earlier work of the authors on the controllability problem for the same class of systems. A full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions. It is also shown that controllability implies stabilizability for th...

This article first introduces an extension of the classical cumulative constraint: each task is no more a rectangle but rather a sequence of contiguous trapezoid sub-tasks with variable duration and heights. The resource function is no more constant but is a positive or negative piecewise linear function of time. Finally, a task is no more pre-assigned to one resource, but to a task corresponds...

Electronic exchanges are double-sided marketplaces that allow multiple buyers to trade with multiple sellers, with aggregation of demand and supply across the bids to maximize the revenue in the market. Two important issues in the design of exchanges are (1) trade determination (determining the number of goods traded between any buyerseller pair) and (2) pricing. In this paper we address the tr...

By providing a counterexample we show that there exists a shift-invariant space S generated by a piecewise linear function such that the union of the corresponding scaled spaces Sh (h > 0) is dense in C0(R) but S does not contain a stable and locally supported partition of unity. This settles a question raised by C. de Boor and R. DeVore a decade ago.