Hassan Boualem

On What Is the Almost-Near Principle

Abstract We introduce a class of functions satisfying what we call the Almost-Near property, or briefly the (AN) property. The motivation of this investigation is provided by the phenomenon “almost implies near” which appears in many various situations. We study some elementary properties of these functions and develop several examples (such as polynomial functions, complex exponential and covering maps).

To Be (a Circle) or Not to Be

Summary We begin with a high school exercise, determining whether a particular equation describes an arc of a circle. We give several proofs that it does not, exploring many properties of circles along the way. Yet the curve is the arc of a conic.We then explore which equations of a generalized family are arcs of conics and give some properties of the resulting Lamé curves.

Exemples de pseudo-métriques compatibles avec une forme symplectique; cas particulier des structures pseudo-kählériennes

Resume Nous donnons une methode explicite pour construire des varietes symplectiques munies d’une pseudo-metrique compatible. Elles apparaissent comme espace total d’une classe speciale de fibrations etudiee en [1]. Parmi elles, quelques exemples de varietes pseudo-kahleriennes compactes a courbure non nulle sont exhibes.