Displaying similar documents to “A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations”

error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ...

Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations

Luís Balsa Bicho, António Ornelas (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove of vector minimizers () =  (||) to multiple integrals ∫ ((), |()|)  on a  ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a  : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...

Trivial Cases for the Kantorovitch Problem

Serge Dubuc, Issa Kagabo, Patrice Marcotte (2010)

RAIRO - Operations Research

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Let and be two compact spaces endowed with respective measures and satisfying the condition . Let be a continuous function on the product space . The mass transfer problem consists in determining a measure on whose marginals coincide with and , and such that the total cost be minimized. We first show that if the cost function is decomposable, i.e., can be represented as the sum of two continuous functions defined on and , respectively, then every feasible measure is optimal....

Hydrodynamic limit of a d-dimensional exclusion process with conductances

Fábio Júlio Valentim (2012)

Annales de l'I.H.P. Probabilités et statistiques

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Fix a polynomial of the form () = + ∑2≤≤    =1 with (1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on 𝕋 d , with conductances given by special class of functions, is described by the unique weak solution of the non-linear parabolic partial differential equation = ∑    ...

Hereditary properties of words

József Balogh, Béla Bollobás (2010)

RAIRO - Theoretical Informatics and Applications

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Let be a hereditary property of words, , an infinite class of finite words such that every subword (block) of a word belonging to is also in . Extending the classical Morse-Hedlund theorem, we show that either contains at least words of length for every  or, for some , it contains at most words of length for every . More importantly, we prove the following quantitative extension of this result: if has words of length then, for every , it contains at most ⌈( + 1)/2⌉⌈( + 1)/2⌈...

Means in complete manifolds: uniqueness and approximation

Marc Arnaudon, Laurent Miclo (2014)

ESAIM: Probability and Statistics

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Let be a complete Riemannian manifold,  ∈ ℕ and  ≥ 1. We prove that almost everywhere on  = ( ,, ) ∈  for Lebesgue measure in , the measure μ ( x ) = N ∑ k = 1 N x k μ ( x ) = 1 N ∑ k = 1 N δ x k has a unique–mean (). As a consequence, if  = ( ,, ) is a -valued random variable with absolutely continuous law, then almost surely (()) has a unique –mean. In particular if ( ...

Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory

Elena Di Bernardino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur (2013)

ESAIM: Probability and Statistics

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This paper deals with the problem of estimating the level sets () =  {() ≥ }, with  ∈ (0,1), of an unknown distribution function on ℝ . A plug-in approach is followed. That is, given a consistent estimator of , we estimate () by () =  { () ≥ }. In our setting, non-compactness property is required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric...

Upper large deviations for maximal flows through a tilted cylinder

Marie Theret (2014)

ESAIM: Probability and Statistics

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We consider the standard first passage percolation model in ℤ for  ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to and whose height is () for a certain height function . We denote this maximal flow by (respectively ). We emphasize the fact that the cylinder may be tilted. We look at the probability that...

Universality in the bulk of the spectrum for complex sample covariance matrices

Sandrine Péché (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider complex sample covariance matrices = (1/)* where is a × random matrix with i.i.d. entries , 1 ≤ ≤ , 1 ≤ ≤ , with distribution . Under some regularity and decay assumptions on , we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where → ∞ and lim→∞ / = for any real number ∈ (0, ∞).

Integers in number systems with positive and negative quadratic Pisot base

Z. Masáková, T. Vávra (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We consider numeration systems with base and − , for quadratic Pisot numbers and focus on comparing the combinatorial structure of the sets Z and Z of numbers with integer expansion in base , resp. − . Our main result is the comparison of languages of infinite words and coding the ordering of distances between consecutive - and (− )-integers. It turns out that for a class of roots of − − , the languages coincide, while for other...