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**publisher and metadata sources**).Each measurable map of an open set U subset of R-n to R-n is equal almost everywhere to the gradient of a continuous almost everywhere differentiable function defined on R-n that vanishes, together… Continue Reading

We provide a simple example showing that the tangential derivative of a continuous function φ can vanish everywhere along a curve while the variation of φ along this curve is nonzero. We give… Continue Reading

In the present note, we examine the behavior of some homo\-thecy-invariant differentiation basis of rectangles in the plane satisfying the following requirement: for a given rectangle to belong to… Continue Reading

A compact subset S of R^N is removable for the equation div v = 0 if every bounded Borel vector field whose distributional divergence vanishes outside S, has a zero distributional divergence in the… Continue Reading

An m charge in the n dimensional Euclidean space is a linear functional acting on m dimensional polyhedral chains and satisfying the following continuity condition. The value of the linear functional… Continue Reading

On etudie ici la repartition des emplois des « quantifieurs » multus et magnus dans le theâtre de Plaute et Terence, et la relation de ces « quantifieurs » a la quantification et aux interrogatifs… Continue Reading

Giving the space N-m(R-n) of m-dimensional normal currents a suitable topology, we define charges as continuous linear functionals. A continuous differential form omega : R-n -> Lambda R-m(n) acting… Continue Reading

We show that, given some lacunary sequence of angles $\mathbf{\theta}=(\theta_j)_{j\in\N}$ not converging too fast to zero, it is possible to build a rare differentiation basis $\mathcal{B}$ of… Continue Reading

We show that any closed set E having a sigma-finite (n - 1)-dimensional Hausdorff measure does not support the nonzero distributional divergence of a continuous vector field; in particular it has the… Continue Reading