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12 results on '"Instituto de Ciencias Matemàticas [Madrid] (ICMAT)"'

1. On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems

Author

Ivan Bardet, Cambyse Rouzé, David Pérez-García, Angelo Lucia, Angela Capel, Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), California Institute of Technology (CALTECH), Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM), Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), Ivan Bardet is supported by French A.N.R. grant: ANR-14-CE25-0003 'StoQ'. Angela Capel is partially supported by a La Caixa-Severo Ochoa grant (ICMAT Severo Ochoa project SEV-2011-0087, MINECO) and Angela Capel and David Perez Garcia acknowledge support from MINECO (grant MTM2017-88385-P) and from Comunidad de Madrid (grantQUITEMAD-CM, ref. P2018/TCS-4342). Angelo Lucia acknowledges support from the Walter Burke Institute for Theoretical Physics in the form of the Sherman Fairchild Fellowship as well as support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant PHY-1733907), and from the BBVA Fundation.This project has received funding from the European Research Council (ERC) under theEuropean Union’s Horizon 2020 research and innovation programme (grant agreementNo 648913). Cambyse Rouzé acknowledges financial support from the TUM university Foundation Fellowship and by the DFG cluster of excellence 2111 (Munich Center for Quantum Science and Technology)., Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Security, Cryptology and Transmissions (SECRET), Instituto de Ciencias Matemàticas [Madrid], Consejo Superior de Investigaciones Científicas [Spain] (CSIC), Universidad Complutense de Madrid [Madrid] (UCM), and Technische Universität München [München] (TUM)

Subjects
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, Gibbs state, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Entropy (classical thermodynamics), symbols.namesake, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], 0103 physical sciences, 0101 mathematics, Gibbs measure, Mixing (physics), Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematical physics, Mathematics, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), 010102 general mathematics, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Sobolev space, symbols, Dissipative system, 010307 mathematical physics, Constant (mathematics), Quantum Physics (quant-ph), Hamiltonian (control theory)
Abstract

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure, via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic Sobolev constant associated to the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular we show that for the heat-bath dynamics for 1D systems, the modified logarithmic Sobolev constant is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy., 28 pages, 4 figures. Included some additional comments and updated results in light of recent advances in the literature

Published
2021
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2. Parabolic subgroups acting on the additional length graph

Author

Yago Antolín, María Cumplido, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), University of Sevilla, Spanish GovernmentEuropean CommissionMTM2014-53810-C2-01MTM2017-82690-PMTM2016-76453-C2-1-PSpanish Government through the 'Severo Ochoa Programme for Centres of Excellence in RD'SEV-2015-0554European CommissionMTM2016-76453-C2-1-P, Universidad de Sevilla. Departamento de Álgebra, and Universidad de Sevilla. FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía

Subjects
Pure mathematics, media_common.quotation_subject, Braid group, Garside groups, artin-tits groups, Group Theory (math.GR), acylindrically hyperbolic groups, parabolic subgroups, 01 natural sciences, Mathematics::Group Theory, Álgebra, 0103 physical sciences, relative growth, FOS: Mathematics, Uniform boundedness, braid groups, 0101 mathematics, [MATH]Mathematics [math], Mathematics, media_common, growth of groups, Grupos (Matemáticas), Sequence, Group (mathematics), 010102 general mathematics, Infinity, 20F36, 20F65, Artin groups, Generating set of a group, Graph (abstract data type), 010307 mathematical physics, Geometry and Topology, Element (category theory), Mathematics - Group Theory
Abstract

Let $A\neq A_1, A_2, I_{2m}$ be an irreducible Artin--Tits group of spherical type. We show that periodic elements of $A$ and the elements preserving some parabolic subgroup of $A$ act elliptically on the additional length graph $\mathcal{C}_{AL}(A)$, an hyperbolic, infinite diameter graph associated to $A$ constructed by Calvez and Wiest to show that $A/Z(A)$ is acylindrically hyperbolic. We use these results to find an element $g\in A$ such that $\langle P,g \rangle\cong P* \langle g \rangle$ for every proper standard parabolic subgroup $P$ of $A$. The length of $g$ is uniformly bounded with respect to the Garside generators, independently of $A$. This allows us to show that, in contrast with the Artin generators case, the sequence $\{\omega(A_n,\mathcal{S})\}_{n\in \mathbb{N}}$ of exponential growth rates of braid groups with respect to the Garside generating set, goes to infinity., Comment: 19 pages, 2 figures

Published
2021
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3. Mapping properties of operator-valued pseudo-differential operators

Author

Runlian Xia, Xiao Xiong, Laboratoire de Mathématiques (LM-Brest), Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Institute for Advanced Study [Tsinghua], Tsinghua University [Beijing] (THU), School of Mathematics and Statistics, and University of New South Wales [Sydney] (UNSW)

Subjects
010102 general mathematics, Mathematics - Operator Algebras, Torus, Differential operator, 01 natural sciences, Functional Analysis (math.FA), Combinatorics, Sobolev space, Mathematics - Functional Analysis, Atomic decomposition, Operator (computer programming), Mathematics - Classical Analysis and ODEs, 0103 physical sciences, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Primary: 46L52, 42B30. Secondary: 46L07, 47L65, Computer Science::Symbolic Computation, 010307 mathematical physics, 0101 mathematics, [MATH]Mathematics [math], Operator Algebras (math.OA), Analysis, Mathematics
Abstract

In this paper, we investigate the mapping properties of pseudo-differential operators with operator-valued symbols. Thanks to the smooth atomic decomposition of the operator-valued Triebel-Lizorkin spaces $F_1^{\alpha,c}(\mathbb{R}^d,\mathcal{M})$ obtained in our previous paper, we establish the $F_1^{\alpha,c}$-regularity of regular symbols for every $\alpha\in \mathbb{R}$, and the $F_1^{\alpha,c}$-regularity of forbidden symbols for $\alpha>0$. As applications, we obtain the same results on the usual and quantum tori., Comment: 37 pages

Published
2018
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4. Structure and enumeration of K4-minor-free links and link diagrams

Author

Dimitrios M. Thilikos, Vasiliki Velona, Juanjo Rué, Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Department of Mathematics [Athens], National and Kapodistrian University of Athens (NKUA), Algorithmes, Graphes et Combinatoire (ALGCO), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), and ANR-17-CE23-0010,ESIGMA,Efficacité et structure pour les applications de la fouille de graphes(2017)

Subjects
links, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], 0211 other engineering and technologies, knots, 0102 computer and information sciences, 02 engineering and technology, series-parallel graphs, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Computer science--Mathematics, 01 natural sciences, Connected sum, Combinatorics, Series-parallel graphs, asymptotic enumeration, map enumeration, Informàtica--Matemàtica, generating functions, Enumeration, Discrete Mathematics and Combinatorics, Unknot, Subdivision, Mathematics, Knots, Map enumeration, 021103 operations research, business.industry, Applied Mathematics, Torus, Matemàtiques i estadística::Matemàtica discreta [Àrees temàtiques de la UPC], Asymptotic enumeration, Graph, Generating functions, 010201 computation theory & mathematics, business, Links
Abstract

We study the class L of link types that admit a K4-minor-free diagram, i.e., they can be projected on the plane so that the resulting graph does not contain any subdivision of K4. We prove that L is the closure of a subclass of torus links under the operation of connected sum. Using this structural result, we enumerate L and subclasses of it, with respect to the minimal number of crossings or edges in a projection of L ∈ L . Further, we enumerate (both exactly and asymptotically) all connected K4-minor-free link diagrams, all minimal connected K4-minor-free link diagrams, and all K4-minor-free diagrams of the unknot.

Published
2018
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5. Self-improving properties for abstract Poincaré type inequalities

Author

José María Martell, Frédéric Bernicot, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Ministerio de Economía y Competitividad (España), Martell, José María, and Martell, José María [0000-0001-6788-4769]

Subjects
Generalized Poincar e-Sobolev inequalities, Computer Science::Machine Learning, General Mathematics, Dyadic cubes, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Computer Science::Digital Libraries, 01 natural sciences, semigroups, Statistics::Machine Learning, symbols.namesake, 0103 physical sciences, 46E35, John-Nirenberg inequalities, Direct proof, 0101 mathematics, Lp space, Self-improving properties, Mathematics, BMO and Lipschitz spaces, Conjecture, Euclidean space, Applied Mathematics, 010102 general mathematics, 1. No poverty, Lipschitz continuity, pseudo-Poincaré inequalities, Algebra, Elliptic operator, Pseudo-Poincare inequalities, Mathematics - Classical Analysis and ODEs, Poincaré conjecture, Computer Science::Mathematical Software, symbols, generalized Poincaré-Sobolev inequalities, 010307 mathematical physics
Abstract

We study self-improving properties in the scale of Lebesgue spaces of generalized Poincar e inequalities in the Euclidean space. We present an abstract setting where oscillations are given by certain operators (e.g., approximations of the identity, semigroups or mean value operators) that have o -diagonal decay in some range. Our results provide a uni ed theory that is applicable to the classical Poincar e inequalities and furthermore it includes oscillations de ned in terms of semigroups associated with second order elliptic operators as those in the Kato conjecture. In this latter situation we obtain a direct proof of the John-Nirenberg inequality for the associated BMO and Lipschitz spaces of [HMay, HMM], The second author was supported by MINECO Grant MTM2010-16518 and ICMAT Severo Ochoa project SEV-2011-0087

Published
2014
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6. Stability estimates for the Calder\'on problem with partial data

Author

Pedro Caro, David Dos Santos Ferreira, Alberto Ruiz, Department of Mathematics and Statistics [Helsinki], Falculty of Science [Helsinki], University of Helsinki-University of Helsinki, Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Departamento de Matemáticas [Madrid], Universidad Autonoma de Madrid (UAM), Helsingin yliopisto = Helsingfors universitet = University of Helsinki-Helsingin yliopisto = Helsingfors universitet = University of Helsinki, Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), and Universidad Autónoma de Madrid (UAM)

Subjects
Convex hull, Bounded set, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Dimension (graph theory), Open set, Mathematics::Analysis of PDEs, Type (model theory), Inverse problem, Mathematics::Spectral Theory, 01 natural sciences, 010101 applied mathematics, Mathematics - Analysis of PDEs, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, Uniqueness, 0101 mathematics, Analysis, Mathematics
Abstract

International audience; This is a follow-up of a previous article where we proved local stability estimates for a potential in a Schr\"odinger equation on an open bounded set in dimension $n=3$ from the Dirichlet-to-Neumann map with partial data. The region under control was the penumbra delimited by a source of light outside of the convex hull of the open set. These local estimates provided stability of log-log type corresponding to the uniqueness results in Calder\'on's inverse problem with partial data proved by Kenig, Sj\"ostrand and Uhlmann. In this article, we prove the corresponding global estimates in all dimensions higher than three. The estimates are based on the construction of solutions of the Schr\"odinger equation by complex geometrical optics developed in the anisotropic setting by Dos Santos Ferreira, Kenig, Salo and Uhlmann to solve the Calder\'on problem in certain admissible geometries.

Published
2016
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7. Vertical versus conical square functions

Author

José María Martell, Pascal Auscher, Steve Hofmann, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), University of Missouri [Columbia] (Mizzou), University of Missouri System, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M)

Subjects
elliptic operators, Applied Mathematics, General Mathematics, 010102 general mathematics, Mathematical analysis, extrapolation, MSC 2010: 42B25, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Conical surface, 01 natural sciences, Vertical square functions, Square (algebra), Elliptic operator, Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, 0103 physical sciences, Classical Analysis and ODEs (math.CA), FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 010307 mathematical physics, 0101 mathematics, conical square functions, Analysis of PDEs (math.AP), Mathematics
Abstract

We study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator., Comment: 21 pages

Published
2012
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8. On Euler’s decomposition formula for $$q$$ q MZVs

Author

Kurusch Ebrahimi-Fard, Dominique Manchon, Jaime Castillo Medina, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M)

Subjects
Pure mathematics, Algebra and Number Theory, Mathematics - Number Theory, Generalization, Mathematics::Number Theory, 010102 general mathematics, Jackson integral, Rota–Baxter algebra, 01 natural sciences, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], symbols.namesake, Number theory, Fourier analysis, 0103 physical sciences, FOS: Mathematics, Decomposition (computer science), Euler's formula, symbols, Number Theory (math.NT), 010307 mathematical physics, 0101 mathematics, [MATH]Mathematics [math], Mathematics
Abstract

We derive a $$q$$ -generalization of Euler’s decomposition formula for the $$q$$ MZVs recently introduced by Y. Ohno, J. Okuda, and W. Zudilin. This answers a question posed by these authors in J Number Theory 132, 144–155 (2012).

Published
2015
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9. Unfolding the double shuffle structure of q-multiple zeta values

Author

Dominique Manchon, Jaime Castillo-Medina, Kurusch Ebrahimi-Fard, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M)

Subjects
Pure mathematics, Number theory, 11M32, 39A13, Mathematics - Number Theory, General Mathematics, Regularization (physics), Jackson integral, FOS: Mathematics, Number Theory (math.NT), [MATH]Mathematics [math], 16. Peace & justice, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Mathematics
Abstract

We exhibit the double q-shuffle structure for the qMZVs recently introduced by Y. Ohno, J. Okuda and W. Zudilin., Comment: Submitted. Added paragraphs (5.2 and 5.3) on handling non-modified qMZVs. Red internal comment removed

Published
2013
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10. The probability of planarity of a random graph near the critical point

Author

Juanjo Rué, Marc Noy, Vlady Ravelomanana, Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya [Barcelona] (UPC), Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), and Alain Goupil and Gilles Schaeffer

Subjects
Discrete mathematics, Random graph, General Computer Science, Structure (category theory), planar cubic multigraphs, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Mathematical proof, Planarity testing, Theoretical Computer Science, Combinatorics, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Critical point (set theory), Random regular graph, analytic combinatorics, Discrete Mathematics and Combinatorics, Analytic combinatorics, Constant (mathematics), random graphs, Mathematics
Abstract

Erdős and Rényi conjectured in 1960 that the limiting probability $p$ that a random graph with $n$ vertices and $M=n/2$ edges is planar exists. It has been shown that indeed p exists and is a constant strictly between 0 and 1. In this paper we answer completely this long standing question by finding an exact expression for this probability, whose approximate value turns out to be $p ≈0.99780$. More generally, we compute the probability of planarity at the critical window of width $n^{2/3}$ around the critical point $M=n/2$. We extend these results to some classes of graphs closed under taking minors. As an example, we show that the probability of being series-parallel converges to 0.98003. Our proofs rely on exploiting the structure of random graphs in the critical window, obtained previously by Janson, Łuczak and Wierman, by means of generating functions and analytic methods. This is a striking example of how analytic combinatorics can be applied to classical problems on random graphs.

Published
2013

11. Stability estimates for the Radon transform with restricted data and applications

Author

Pedro Caro, David Dos Santos Ferreira, Alberto Ruiz, Department of Mathematics and Statistics [Helsinki], Falculty of Science [Helsinki], University of Helsinki-University of Helsinki, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Departamento de Matemáticas [Madrid], Universidad Autonoma de Madrid (UAM), Instituto de Ciencias Matemàticas [Madrid] (ICMAT), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M)

Subjects
Mathematics - Analysis of PDEs, Radon transform, Mathematics - Classical Analysis and ODEs, General Mathematics, Norm (mathematics), Mathematical analysis, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inverse, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, Mathematics, Analysis of PDEs (math.AP)
Abstract

In this article, we prove a stability estimate going from the Radon transform of a function with limited angle-distance data to the $L^p$ norm of the function itself, under some conditions on the support of the function. We apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data., Comment: 37 pages

Published
2012
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12. On an extension of Knuth's rotation correspondence to reduced planar trees

Author

Dominique Manchon, Kurusch Ebrahimi-Fard, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Carlos III de Madrid [Madrid] (UC3M), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)

Subjects
Algebra and Number Theory, Binary tree, Mathematics::Combinatorics, Structure (category theory), Extension (predicate logic), Computer Science::Computational Geometry, Hopf algebra, Space (mathematics), Combinatorics, Planar, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Bijection, FOS: Mathematics, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO), [MATH]Mathematics [math], Rotation (mathematics), Mathematical Physics, Mathematics
Abstract

International audience; We present a bijection from planar reduced trees to planar rooted hypertrees, which extends Knuth's rotation correspondence between planar binary trees and planar rooted trees. The operadic counterpart of the new bijection is explained. Related to this, the space of planar reduced forests is endowed with a combinatorial Hopf algebra structure. The corresponding structure on the space of planar rooted hyperforests is also described.

Published
2012
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