Problem-based learning is particularly suitable in fields like Mathematics. It is quite usual to find abstract descriptions of solving methods to express mathematical knowledge. However, these descriptions happen to be somewhat hard for students. For instance, when a learner faces the integration-by-parts method, one possibility is to try to understand the general formula (by using the abstract...

We developed a system the purpose of which is obtaining a robot able to emulate the strategies used by a human facing a problem-solving task. We have been able to solve this problem within a very particular psychological setting, in which the human behaviour can be interpreted as ‘observables’ of his/her problem-solving strategy. Our solution encompasses the one of yet another problem, namely, ...

Electromagnetism-like algorithm (EM) is a population-based metaheuristic which has been proposed to solve continuous problems effectively. In this paper, we present a new meta-heuristic that uses the EM methodology to solve the single machine scheduling problem. Single machine scheduling is a combinatorial optimization problem. Schedule representation for our problem is based on random keys. Be...

The aim of this short note is to show that the class of problem involving kinetic or thermo–kinetic constraints in addition to the usual stoechiometric one is non convex.

Motivated by the parallelism existing between the puzzles of classical physics at the beginning of the XXth century and the current paradoxes in the search of a quantum theory of gravity, we give, in analogy with Planck’s black body radiation problem, a solution for the exact Hawking flux of evaporating ReissnerNordström black holes. Our results show that when back-reaction effects are fully ta...

Given a simple graph G with a vertex set V and a set of "requirements" {rvw \ v , w E V}, we consider a problem to find a Hamilton cycle minimizing an objective function similar to that in the optimum requirement spanning tree (ORST) problem studied by Hu. And we show that a particular Hamilton cycle C" which is explicitly definable is a solution to the problem when G is complete and { r v w } ...

In this paper we consider an initial and boundary value problem modeling the self-propelled motion of solids in a bi-dimensional viscous incompressible uid. The self-propelling mechanism, consisting in appropriate deformations of the solids, is a simpli ed model for the propulsion mechanism of sh-like swimmers. The governing equations are composed of the Navier-Stokes equations for the uid, cou...

In this paper, the existence of step-like contrast structure for a class of singularly perturbed optimal control problem is shown by the contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. Finally, an example is presented to show the result. 2000 Mathematics S...

This paper deals with the convergence of the algorithm built on the auxiliary problem principle for solving a class of pseudomonotone type mixed variational-like inequalities. The convergence criteria of this method are presented under a joint pseudo-Dunn property or a joint strong pseudomonotonicity assumption on the operators involved in the mixed variational-like inequality problem. Moreover...

We consider a nonatomic congestion game on a connected graph, with several classes of players. Each player wants to go from its origin vertex to its destination vertex at the minimum cost and all players of a given class share the same characteristics: cost functions on each arc, and origin-destination pair. Under some mild conditions, it is known that a Nash equilibrium exists, but the computa...