Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting. In the case of constant advection, these methods and the traditional semi-Lagrangian ones are proven to be equivalent, but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity. In the non constant advection case...

2 II.Acknowledgment 3 III.Table of

For upper semicontinuous finite-dimensional set-valued mappings with either convex closed or aspheric closed values we prove the existence of special continuous e -approximations that point-wise converge to a Borel measurable selector of the set-valued mapping as e tends to zero. For convex-valued case the convergence holds on the entire domain while for aspheric-valued case — on a certain coun...

Zaj́ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any realvalued function on a normed linear space, the se...

X ω = 1. An upper semicontinuous function φ : X → [−∞,+∞) is called ω-plurisubharmonic (ω-psh) if φ ∈ L(X) and ωφ := ω + dd φ ≥ 0. By PSH(X,ω) (resp. PSH(X,ω)) we denote the set of ω-psh (resp. negative ω-psh) functions on X . The complex Monge-Ampère equation ω u = fω n was solved for smooth positive f in the fundamental work of S. T. Yau (see [Yau]). Later S. Kolodziej showed that there exist...

In this work, we improve the approach of [15] to nonlinear error bounds for lower semicontinuous functions on complete metric spaces, an approach consisting in reducing the nonlinear case to the linear one through a change of metric. This improvement is basically a technical one, and allows dealing with local error bounds in an appropriate way. We present some consequences of the general result...

Semi-supervised wrapper methods are concerned with building effective supervised classifiers from partially labeled data. Though previous works have succeeded in some fields, it is still difficult to apply semi-supervised wrapper methods to practice because the assumptions those methods rely on tend to be unrealistic in practice. For practical use, this paper proposes a novel semi-supervised wr...

We characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales.

Article history: Received 28 July 2007 Received in revised form 30 April 2008 Accepted 1 May 2008 Available online 9 May 2008