| 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. |
- Adiprasito, Karim, et al.
(författare)
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Connectivity of pseudomanifold graphs from an algebraic point of view
- 2015
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Ingår i: Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science. - : Elsevier. - 0706-1994. ; 353:12, s. 1061-1065
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Tidskriftsartikel (refereegranskat)abstract
- The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, including Balinski, Barnette, Athanasiadis, and Bjorner. In this note, we provide a unifying approach that allows us to obtain more general results. Moreover, we provide a relation to commutative algebra by relating connectivity problems to graded Betti numbers of the associated Stanley-Reisner rings.
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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- Groves, Mark D., et al.
(författare)
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Periodic solitons for the elliptic-elliptic focussing Davey-Stewartson equations
- 2016
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Ingår i: Comptes Rendus Mathématique. - : Elsevier BV. - 1631-073X. ; 354:5, s. 486-492
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Tidskriftsartikel (refereegranskat)abstract
- We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal spatial direction and are periodic in the transverse spatial direction, is established using dynamical systems arguments. We also show that the line soliton is linearly unstable with respect to perturbations in the transverse direction.
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| 7. |
- Groves, Mark D., et al.
(författare)
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Variational existence theory for hydroelastic solitary waves : Une théorie variationnelle d'existence d'ondes solitaires hydroélastiques
- 2016
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Ingår i: Comptes Rendus Mathématique. - : Elsevier BV. - 1631-073X. ; 354:11, s. 1078-1086
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents an existence theory for solitary waves at the interface between a thin ice sheet (modelled using the Cosserat theory of hyperelastic shells) and an ideal fluid (of finite depth and in irrotational motion) for sufficiently large values of a dimensionless parameter γ. We establish the existence of a minimiser of the wave energy E subject to the constraint I=2μ, where I is the horizontal impulse and 0<μ≪1, and show that the solitary waves detected by our variational method converge (after an appropriate rescaling) to solutions to the nonlinear Schrödinger equation with cubic focussing nonlinearity as μ↓0.
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| 8. |
- 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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| 9. |
- 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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| 10. |
- 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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