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 Comptes Rendus : MathematiqueNumber of Followers: 0     Open Access journal ISSN (Print) 1631-073X - ISSN (Online) 1778-3569 Published by
• Óscar Domínguez; Mario Milman - Sparse Brudnyi and
John–Nirenberg Spaces

• Abstract: A generalization of the theory of Y. Brudnyi [7], and A. and Y. Brudnyi [5, 6], is presented. Our construction connects Brudnyi’s theory, which relies on local polynomial approximation, with new results on sparse domination. In particular, we find an analogue of the maximal theorem for the fractional maximal function, solving a problem proposed by Kruglyak–Kuznetsov. Our spaces shed light on the structure of the John–Nirenberg spaces. We show that SJN p (sparse John–Nirenberg space) coincides with L p ,1<p<∞. This characterization yields the John–Nirenberg inequality by extrapolation and is useful in the theory of commutators.
PubDate: Fri, 08 Oct 2021 00:00:00 +000

• +FP++2+ &rft.title=Comptes+Rendus+:+Mathematique&rft.issn=1631-073X&rft.date=2021&rft.volume=">Robert D. Gray; Benjamin Steinberg - Free inverse monoids are not FP 2

• Abstract: We give a topological proof that a free inverse monoid on one or more generators is neither of type left-FP 2 nor right-FP 2 . This strengthens a classical result of Schein that such monoids are not finitely presented as monoids.
PubDate: Fri, 08 Oct 2021 00:00:00 +000

• Jing Zhang - Levi Problem: Complement of a closed subspace in a Stein
space and its applications

• Abstract: Let Y be an open subset of a Stein space X. We show that if Y is locally Stein and the complement X-Y is a closed subspace of X, then Y is Stein. We also discuss the applications of the theorem to open subsets Y whose boundaries in X are not closed subspaces of X. For example, we show that if for every boundary point P∈∂Y, there is a closed subspace H of pure codimension 1 in X such that P∈H, H∩Y=∅ and X-H is locally Stein, then Y is Stein.
PubDate: Fri, 08 Oct 2021 00:00:00 +000

• Chandranandan Gangopadhyay; Ronnie Sebastian - Nef cones of some Quot
schemes on a Smooth Projective Curve

• Abstract: Let C be a smooth projective curve over ℂ. Let n,d≥1. Let ð’¬ be the Quot scheme parameterizing torsion quotients of the vector bundle ð’ª C n of degree d. In this article we study the nef cone of ð’¬. We give a complete description of the nef cone in the case of elliptic curves. We compute it in the case when d=2 and C very general, in terms of the nef cone of the second symmetric product of C. In the case when n≥d and C very general, we give upper and lower bounds for the Nef cone. In general, we give a necessary and sufficient criterion for a divisor on ð’¬ to be nef.
PubDate: Fri, 08 Oct 2021 00:00:00 +000

• Christophe Eyral; Tadeusz Mostowski et al. - On some properties of the
Łojasiewicz exponent

• Abstract: In this note, we investigate the behaviour of the Łojasiewicz exponent under hyperplane sections and its relation to the order of tangency.
PubDate: Fri, 08 Oct 2021 00:00:00 +000

• Ilia Smilga - New sequences of non-free rational points

• Abstract: We exhibit some new infinite families of rational values of τ, some of them squares of rationals, for which the group or even the semigroup generated by the matrices (1101) and  (10τ1) is not free.
PubDate: Fri, 08 Oct 2021 00:00:00 +000

• Ronan Le Guével - Exponential inequalities for the supremum of some
counting processes and their square martingales

• Abstract: Nous établissons ici des inégalités exponentielles pour le supremum de martingales et de martingales carrées issues de processus de comptage, ainsi que pour le processus d’oscillation de ces processus. Ces inégalités, qui jouent un rôle essentiel dans le contrôle d’erreur de certaines procédures statistiques, s’appliquent à des processus de comptage non-explosifs généraux, comme les processus de Poisson, de Hawkes ou encore les processsus de Cox. Quelques applications aux U-statistiques sont aussi abordées dans cet article.
PubDate: Fri, 08 Oct 2021 00:00:00 +000

• Youpei Zhang; Xianhua Tang et al. - Anisotropic Choquard problems with
Stein–Weiss potential: nonlinear patterns and stationary waves

• Abstract: Weighted inequality theory for fractional integrals is a relatively less known branch of calculus that offers remarkable opportunities to simulate interdisciplinary processes. Basic weighted inequalities are often associated to Hardy, Littlewood and Sobolev [6, 11], Caffarelli, Kohn and Nirenberg [4], respectively to Stein and Weiss [12]. A key attempt in the present paper is to prove a Stein–Weiss inequality with lack of symmetry and variable exponents. We quantify the defect of symmetry of the potential by considering the gap between the minimum and the maximum of the variable exponent. We conclude our work with a section dealing with the existence of stationary waves for a class of nonlocal problems with Choquard nonlinearity and anisotropic Stein–Weiss potential.
PubDate: Wed, 06 Oct 2021 00:00:00 +000

• David Gontier - Spectral properties of periodic systems cut at an angle

• Abstract: We consider a semi-periodic two-dimensional Schrödinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the incommensurable case, there are no gaps: the gaps of the bulk operator are filled with edge spectrum.
PubDate: Wed, 06 Oct 2021 00:00:00 +000

• Nikolay Kuznetsov - Characterization of balls via solutions of the
modified Helmholtz equation

• Abstract: A theorem characterizing analytically balls in the Euclidean space ℝ m is proved. For this purpose positive solutions of the modified Helmholtz equation are used instead of harmonic functions applied in previous results. The obtained Kuran type theorem is based on the volume mean value property of solutions to this equation.
PubDate: Wed, 06 Oct 2021 00:00:00 +000

• Andrei S. Rapinchuk; Igor A. Rapinchuk - Finiteness theorems for algebraic
tori over function fields

• Abstract: Nous présentons plusieurs résultats de finitude pour les tores (et, plus généralement, pour les groupes algébriques dont la composante connexe est un tore) définis sur les corps de type fini et les corps de fonctions des variétés algébriques définies sur les corps satisfaisant la condition (F) de Serre.
PubDate: Wed, 06 Oct 2021 00:00:00 +000

• Constantin-Cosmin Todea - BD algebras and group cohomology

• Abstract: BD algebras (Beilinson–Drinfeld algebras) are algebraic structures which are defined similarly to BV algebras (Batalin–Vilkovisky algebras). The equation defining the BD operator has the same structure as the equation for BV algebras, but the BD operator is increasing with degree +1. We obtain methods of constructing BD algebras in the context of group cohomology.
PubDate: Wed, 06 Oct 2021 00:00:00 +000

• Brian Lawrence; Shizhang Li - A counterexample to an optimistic guess

• PubDate: Wed, 06 Oct 2021 00:00:00 +000

• Pierre Deligne - Le critère d’Abel pour la résolubilité par radicaux
d’une équation irréductible de degré premier

• Abstract: Dans sa dernière lettre à Crelle, Abel énonce un critère pour déterminer si une équation irréductible de degré premier est résoluble par radicaux. Sylow dit cet énoncé ambigu et devant être modifié. Nous montrons que le critère donné par Abel est correct tel quel.
PubDate: Fri, 17 Sep 2021 00:00:00 +000

• Bappaditya Bhowmik; Nilanjan Das - Bohr radius and its asymptotic value
for holomorphic functions in higher dimensions

• Abstract: We establish sharp Bohr phenomena for holomorphic functions defined on a bounded balanced domain G in a complex Banach space X, which map into a simply connected domain or a convex domain Ω in the complex plane ℂ. Taking X as the n-dimensional complex plane and G as the open unit polydisk, we consider a version of the Bohr inequality stronger than the above mentioned one and study the exact asymptotic behaviour of the Bohr radius. Explicit lower bounds on the Bohr radii of this type are also provided. Extending a recent result of Liu and Ponnusamy, we further record a refined form of the Bohr inequality for the particular case Ω=ð”», i.e. the open unit disk in ℂ.
PubDate: Fri, 17 Sep 2021 00:00:00 +000

• Iason Efraimidis - Quasiconformal extension for harmonic mappings on
finitely connected domains

• Abstract: We prove that a harmonic quasiconformal mapping defined on a finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits a quasiconformal extension to the whole plane if its Schwarzian derivative is small. We also make the observation that a univalence criterion for harmonic mappings holds on uniform domains.
PubDate: Fri, 17 Sep 2021 00:00:00 +000

• Francesca Bucci; Matthias Eller - The Cauchy–Dirichlet problem for the
Moore–Gibson–Thompson equation

• Abstract: On analyse le problème de Cauchy–Dirichlet pour l’équation de Moore–Gibson–Thompson avec des données non-homogènes. Deux méthodes sont considérées : la théorie des équations hyperboliques et la théorie des semi-groupes d’opérateurs. Il s’agit d’un problème hyperbolique mixte avec une frontière spatiale caractéristique. Par conséquent, les résultats de régularité présentent certaines lacunes par rapport au cas non caractéristique.
PubDate: Fri, 17 Sep 2021 00:00:00 +000

• Nathan Chapelier-Laget - Affine twisted length function

• Abstract: Let W a be an affine Weyl group. In 1987 Jian Yi Shi gave a characterization of the elements w∈W a in terms of Φ + -tuples (k(w,α)) α∈Φ + called the Shi vectors. Using these coefficients, a formula is provided to compute the standard length of W a . In this note we express the twisted affine length function of W a in terms of the Shi coefficients.
PubDate: Fri, 17 Sep 2021 00:00:00 +000

• Arnaud Beauville - A non-hyperelliptic curve with torsion Ceresa class

• Abstract: We exhibit a non-hyperelliptic curve C of genus 3 such that the class of the Ceresa cycle [C]-[-C] in the intermediate Jacobian of JC is torsion.
PubDate: Fri, 17 Sep 2021 00:00:00 +000

• Safari Mukeru - Some applications of the Menshov–Rademacher theorem

• Abstract: Pour une suite de variables aléatoires réelles ou complexes (X n ) et une suite de nombres (a n ), une question importante est de savoir sous quelles conditions la série aléatoire ∑ n=1 ∞ a n X n est convergente presque sûrement. Cette note généralise le théorème classique de Menshov–Rademacher sur la convergence de séries orthogonales aux séries plus générales de variables aléatoires dépendantes et en déduit des conditions suffisantes pour la convergence presque sûre des séries trigonométriques par rapport à des mesures singulières dont la transformée de Fourier tend vers 0 à l’infini avec un taux positif.
PubDate: Fri, 17 Sep 2021 00:00:00 +000

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