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Oleg N. Kirillov and Michael Overton published this article:

Robust Stability at the Swallowtail Singularity

Consider the set of monic fourth-order real polynomials transformed so that the constant term is one. In the three-dimensional space of the coefficients describing this set, the domain of asymptotic stability is bounded by a surface with the Whitney umbrella singularity. The maximum of the real parts of the roots of these polynomials is globally minimized at the Swallowtail singular point of the discriminant surface of the set corresponding to a negative real root of multiplicity four. Motivated by this example, we review recent works on robust stability, abscissa optimization, heavily damped systems, dissipation-induced instabilities, and eigenvalue dynamics in order to point out some connections that appear to be not widely known.

Oleg N. Kirillov and Michael Overton

Frontiers in Mathematical Physics|03 Dec 2013

Source: Société de Calcul Mathématique, SA

Checking an Industrial Process

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The “Mathematical Games“, jointly organized by French Federation of Mathematical Games (FFJM) and Société de Calcul Mathématique (SCM), have existed for five years; the previous ones were:

• In 2008-2009, conception of a bus transportation network in a city, in partnership with Veolia Transport;
• In 2009-2010, conception of an electricity distribution network, in partnership with RTE (Réseau de Transport d’Electricité);
• In 2011-2012, search for the best itinerary by a car, in partnership with the newspaper Auto Plus;
• In 2012-2013, fighting forest fires in Siberia, in partnership with the Paris Firemen Brigade.
• In 2013-2014, checking an industrial process

They deal with the resolution of a “real life” problem, that is a problem of general concern, but simplified in its mathematical contents. Still, the resolution typically requires several months of work.

Candidates may compete individually or as groups, for instance high school classes, or college students, or university students, preparing a “memoir” for the end of their studies.

Two categories of prizes are given:

Individual prizes:

• For the winner: 500 Euros
• For the second: 200 Euros
• For the next three: 100 Euros each.

Prizes for groups:

• For the winner: 500 Euros
• For the second: 200 Euros
• For the next three: 100 Euros each.

The total amount of prizes is therefore 2 000 Euros. The best solutions are published on the web site of FFJM, on the web site of SCM, and on the web sites of the partners. The official announcement of the results and the ceremony for prizes occur during the “Salon de la Culture et des Jeux Mathématiques” (Fair for Mathematical Culture and Games), which is held in Paris, each year, during the month of May.

The winners, previous years, gained considerable notoriety, both in the press and television in their respective countries.