Andriy Yurachkivsky (2012)
ESAIM: Probability and Statistics
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Let, for each , (, ۔) be a random measure on the Borel -algebra in ℝ such that E(, ℝ) < ∞ for all and let (, ۔) be its characteristic function. We call the function ( ,…, ; ,…, ) = of arguments ℕ, , … , , ℝ the of the measure-valued random function (MVRF) (۔, ۔). A...
G. Chavent, K. Kunisch (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the problem : Minimize over , where is a closed convex subset of (Ω), and the last additive term denotes the BV-seminorm of is a linear operator from ∩ into the observation space . We formulate necessary optimality conditions for (). Then we show that () admits, for given regularization parameters α and β, solutions which depend in a stable manner on the data z. Finally we study the asymptotic behavior when α = β → 0. The regularized...
Yves van Gennip, Mark A. Peletier (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We study the -norm of the function 1 on tubular neighbourhoods of curves in . We take the limit of small thickness, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit → 0, containing contributions from the length of the curve (at order ), the ends ( ), and the curvature ( ). The second result is a Γ-convergence result, in which the central curve may vary along...
Erwan Deriaz, Dmitry Kolomenskiy (2012)
ESAIM: Proceedings
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We present a basic althought little known numerical stability condition: for convection equations, the von Neumann stability constraint ∥ ∥ ≤ (1 + Δ) ∥ ∥ drives to the stability condition Δ ≤ Δ with where is an integer linked to the stability domain of the time scheme and ≥ an integer linked to the upwind property of the space discretization...