| 1. |
- Abdulle, Assyr, et al.
(författare)
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Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems
- 2019
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 357:6, s. 545-551
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Tidskriftsartikel (refereegranskat)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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| 2. |
- Aka, Menny, et al.
(författare)
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On metric Diophantine approximation in matrices and Lie groups
- 2015
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 353:3, s. 185-189
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Tidskriftsartikel (refereegranskat)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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| 3. |
- Aleman, Alexandru, et al.
(författare)
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Density of disk algebra functions in de Branges–Rovnyak spaces
- 2017
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 355:8, s. 871-875
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Tidskriftsartikel (refereegranskat)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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| 4. |
- Astashkin, Sergey V., et al.
(författare)
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Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q
- 2018
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Ingår i: Comptes rendus. Mathematique. - : Elsevier. - 1631-073X .- 1778-3569. ; 356:6, s. 661-665
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Tidskriftsartikel (refereegranskat)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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| 5. |
- Klurman, Oleksiy, et al.
(författare)
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A note on multiplicative automatic sequences
- 2019
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Ingår i: Comptes rendus. Mathematique. - : ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER. - 1631-073X .- 1778-3569. ; 357:10, s. 752-755
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Tidskriftsartikel (refereegranskat)abstract
- We prove that any q-automatic completely multiplicative function f: N -> C essentially coincides with a Dirichlet character. This answers a question of J.-P. Allouche and L. Gold-makher and confirms a conjecture of J. Bell, N. Bruin and M. Coons for completely multiplicative functions. Further, assuming GRH, the methods allow us to replace completely multiplicative functions with multiplicative functions.
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| 6. |
- Kozlov, Vladimir, et al.
(författare)
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Trapped modes supported by localized potentials in the zigzag graphene ribbon
- 2016
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Ingår i: Comptes rendus. Mathematique. - : Elsevier. - 1631-073X .- 1778-3569. ; 354:1, s. 63-67
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Tidskriftsartikel (refereegranskat)abstract
- Localized potentials in the Dirac equation for the electron dynamics in a zigzag graphene ribbon are constructed to support trapped modes while the corresponding eigenvalues are embedded into the continuous spectrum. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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| 7. |
- Kurlberg, Pär, et al.
(författare)
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Non-universality of the Nazarov-Sodin constant
- 2015
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 353:2, s. 101-104
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for "arithmetic random waves", i.e. random toral Laplace eigenfunctions.
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| 8. |
- Lu, Li, et al.
(författare)
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Nonlinear artificial viscosity for spectral element methods
- 2019
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 357:7, s. 646-654
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Tidskriftsartikel (refereegranskat)abstract
- We present a filter-based approach to computing artificial viscosities for spectral element methods. A number of applications for this approach are presented.
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| 9. |
- Nenashev, Gleb, 1992-
(författare)
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A note on Fröberg's conjecture for forms of equal degrees
- 2017
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 355:3, s. 272-276
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Tidskriftsartikel (refereegranskat)abstract
- In this note we study ideals generated by generic forms in polynomial rings over any algebraicly closed field of characteristic zero. We prove for many cases that the (d+k)-th graded component of an ideal generated by generic forms of degree d has the expected dimension (given by dimension count). And as a consequence of our result, we obtain that ideals generated by several generic forms of degrees d usually have the expected Hilbert series. The precise form of this expected Hilbert series, in general, is known as Fröberg's conjecture.
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| 10. |
- Solimini, Sergio, et al.
(författare)
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On the defect of compactness in Banach spaces
- 2015
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 353:10, s. 899-903
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Tidskriftsartikel (refereegranskat)abstract
- Concentration compactness methods improve convergence for bounded sequences in Banach spaces beyond the weak-star convergence provided by the Banach-Alaoglu theorem. A further improvement of convergence, known as profile decomposition, is possible up to defect of compactness, a series of "elementary concentrations" defined relative to the action of some group of linear isometric operators. This note presents a general profile decomposition for uniformly convex and uniformly smooth Banach spaces, generalizing the result of one of the authors (S.S.) for Sobolev spaces and of the other (CT. jointly with I. Schindler) for general Hilbert spaces. Unlike in the Hilbert space case, profile decomposition is based not on weak convergence, but on a different mode of convergence, called polar convergence, which coincides with weak convergence if and only if the norm satisfies the known Opial condition, used in the context of fixed point theory for nonexpansive maps.
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