| 1. |
- Gustafsson, Björn, et al.
(author)
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Explicit limits for nonperiodic homogenization and reduction of dimension
- 2002
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In: Comptes rendus. Mathematique. - 1631-073X .- 1778-3569. ; 334:11, s. 977-982
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Journal article (peer-reviewed)abstract
- The aim of this Note is to give explicit limit expressions. for diffusion equations involving a small parameter E, describing both nonperiodic homogenization and reduction of dimension. We consider two kinds of reduction of dimension: the case of plates and the case of thin cylinders. In particular, we give the limit diffusion equation for stratified plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications to fibered materials.
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| 2. |
- Abdulle, Assyr, et al.
(author)
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Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems
- 2019
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In: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 357:6, s. 545-551
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Journal article (peer-reviewed)abstract
- This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell problems, result in an exponential decay of the resonance error.
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| 3. |
- Aka, Menny, et al.
(author)
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On metric Diophantine approximation in matrices and Lie groups
- 2015
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In: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 353:3, s. 185-189
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Journal article (peer-reviewed)abstract
- We study the Diophantine exponent of analytic submanifolds of m x n real matrices, answering questions of Beresnevich, Kleinbock, and Margulis. We identify a family of algebraic obstructions to the extremality of such a submanifold, and give a formula for the exponent when the submanifold is algebraic and defined over Q. We then apply these results to the determination of the Diophantine exponent of rational nilpotent Lie groups.
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| 4. |
- Al Abdulaali, Ahmad, 1981-
(author)
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The extendability of S-plurisubharmonic currents : = Sur le prolongement des courants S-plurisousharmoniques
- 2012
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In: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 350:23-24, s. 1023-1026
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Journal article (other academic/artistic)abstract
- This paper studies the extendability of negative S-plurisubharmonic current of bidimension (p,p) across a (2p-2)-dimensional closed set. Using only the positivity of S, we show that such extensions exist in the case when these obstacles are complete pluripolar, as well as zero sets of C2-plurisubharmoinc functions.
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| 5. |
- Aleman, Alexandru, et al.
(author)
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Density of disk algebra functions in de Branges–Rovnyak spaces
- 2017
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In: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 355:8, s. 871-875
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Journal article (peer-reviewed)abstract
- We prove that functions analytic in the unit disk and continuous up to the boundary are dense in the de Branges–Rovnyak spaces induced by the extreme points of the unit ball of . Together with previous theorems, it follows that this class of functions is dense in any de Branges–Rovnyak space.
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| 6. |
- Astashkin, Sergey V., et al.
(author)
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Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q
- 2018
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In: Comptes rendus. Mathematique. - : Elsevier. - 1631-073X .- 1778-3569. ; 356:6, s. 661-665
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Journal article (peer-reviewed)abstract
- We prove that if 1≤p,q≤∞1≤p,q≤∞, then the spaces Lp+LqLp+Lq and Lp∩LqLp∩Lq are isomorphic if and only if p=qp=q. In particular, L2+L∞L2+L∞ and L2∩L∞L2∩L∞ are not isomorphic, which is an answer to a question formulated in [2].
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| 7. |
- Becker, R., et al.
(author)
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A finite element time relaxation method
- 2011
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In: Comptes Rendus Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 349:5-6, s. 353-356
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Journal article (peer-reviewed)abstract
- We discuss a finite element time-relaxation method for high Reynolds number flows. The method uses local projections on polynomials defined on macroelements of each pair of two elements sharing a face. We prove that this method shares the optimal stability and convergence properties of the continuous interior penalty (CIP) method. We give the formulation both for the scalar convection-diffusion equation and the time-dependent incompressible Euler equations and the associated convergence results. This note finishes with some numerical illustrations. (C) 2010 Academic des sciences. Published by Elsevier Masson SAS. All rights reserved.
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| 8. |
- Benelkourchi, Slimane
(author)
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A Note on the approximation of plurisubharmonic functions
- 2006
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In: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 342:9, s. 647-650
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Journal article (peer-reviewed)abstract
- Let Omega subset of C-n be a strongly hyperconvex domain and Omega(j) be a decreasing sequence of hyperconvex domains such that Omega = (boolean AND Omega(j))degrees. We show that every plurisubharmonic function rho is an element of F-s (Omega) is a limit of an increasing sequence of functions rho(j) is an element of F-a (Omega(j)).
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| 9. |
- Boman, Jan
(author)
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Flatness of distributions vanishing on infinitely many hyperplanes
- 2009
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In: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 347:23-24, s. 1351-1354
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Journal article (peer-reviewed)abstract
- Let be a family of hyperplanes in Rn and let L0 be a limiting hyperplane of {Lk}. Let u be a distribution that satisfies a natural wave front condition and has vanishing restrictions to Lk for all k1. Then u must be flat at L0.
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| 10. |
- Borcea, Julius, et al.
(author)
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Hyperbolic polynomials and spectral order
- 2003
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In: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 337:11, s. 693-698
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Journal article (peer-reviewed)
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