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 Comptes Rendus : MathematiqueJournal Prestige (SJR): 0.757 Citation Impact (citeScore): 1Number of Followers: 0     Open Access journal ISSN (Print) 1631-073X - ISSN (Online) 1778-3569 Published by Académie des sciences  [7 journals]
• q -deformation+of+true-polyanalytic+Bargmann+transforms+when+1\$"> q+ - 1 + &gt; 1 &rft.title=Comptes+Rendus+:+Mathematique&rft.issn=1631-073X&rft.date=2022&rft.volume=">Othmane El Moize; Zouhaïr Mouayn - A q -deformation of true-polyanalytic
Bargmann transforms when q - 1 > 1

• Abstract: We combine continuous q -1 -Hermite Askey polynomials with new 2D orthogonal polynomials introduced by Ismail and Zhang as q-analogs for complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter m. Our construction leads to a new q-deformation of the m-true-polyanalytic Bargmann transform on the complex plane. In the analytic case m=0, the obtained coherent states transform can be associated with the Arïk-Coon oscillator for q ′ =q -1 >1. These result may be used to introduce a q-deformed Ginibre-type point process.
PubDate: Tue, 04 Jan 2022 14:12:43 +000

• Jean Dolbeault; Rupert L. Frank et al. - Logarithmic estimates for
mean-field models in dimension two and the Schrödinger–Poisson system

• Abstract: In dimension two, we investigate a free energy and the ground state energy of the Schrödinger–Poisson system coupled with a logarithmic nonlinearity in terms of underlying functional inequalities which take into account the scaling invariances of the problem. Such a system can be considered as a nonlinear Schrödinger equation with a cubic but nonlocal Poisson nonlinearity, and a local logarithmic nonlinearity. Both cases of repulsive and attractive forces are considered. We also assume that there is an external potential with minimal growth at infinity, which turns out to have a logarithmic growth. Our estimates rely on new logarithmic interpolation inequalities which combine logarithmic Hardy–Littlewood–Sobolev and logarithmic Sobolev inequalities. The two-dimensional model appears as a limit case of more classical problems in higher dimensions.
PubDate: Tue, 04 Jan 2022 14:12:43 +000

• Fatih Say - First-order general differential equation for multi-level
asymptotics at higher levels and recurrence relationship of singulants

• Abstract: We construct a relation between the leading pre-factor function A(z) and the singulants u 0 (z), u 1 (z), and recurrence relation of the singulants at higher levels for the solution of singularly-perturbed first-order ordinary general differential equation with a small parameter via the method of multi-level asymptotics. The particular equation is chosen due to its appearance at every level of multi-level asymptotic approach for the first-order differential equations. By the relations derived by the asymptotic analysis from the equation, Stokes and anti-Stokes lines can be extracted more quickly and so which exponentials of the expansions are actually contributed in each sector of the complex plane can be deduced faster. Multi-level asymptotic analysis of the first-order singular equations and the Stokes phenomenon may be done straightaway from the higher levels of the analysis.
PubDate: Tue, 04 Jan 2022 14:12:43 +000

• Mourad Choulli - Some stability inequalities for hybrid inverse problems

• Abstract: We study some hybrid inverse problems associated to BVP’s for Schrödinger and Helmholtz type equations. The inverse problems we consider consist in the determination of coefficients from the knowledge of internal energy densities. We establish local Lipschitz stability inequalities as well as Hölder stability inequalities.
PubDate: Tue, 04 Jan 2022 14:12:43 +000

• Valentina Casarino; Paolo Ciatti et al. - Uniform pointwise estimates for
ultraspherical polynomials

• Abstract: We prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in arbitrary dimension, and are instrumental in the proof, discussed in a companion paper, of sharp multiplier theorems for those operators.
PubDate: Tue, 04 Jan 2022 14:12:43 +000

• Dimitris Vardakis; Alexander Volberg - Free boundary problems in the
spirit of Sakai’s theorem

• Abstract: Dans le présent article, nous considérons la pléthore de résultats dans l’esprit de théorème de Sakai concernant les fonctions de Schwarz, c’est-à-dire les fonctions holomorphes dans un domaine ouvert Ω satisfaisant S(ζ)=ζ ¯ sur Γ, qui fait partie de la frontière de Ω. Sakai en 1991 a donné une caractérisation complète de la frontière d’un domaine admettant une fonction de Schwarz. Les résultats ci-dessous concernent trois scénarios de généralisation du résultat de Sakai, motivés plutôt par l’application au problème de dynamique complexe étudié dans [13]. À la fin de cette note, nous mentionnons quelques problèmes encore ouverts.
PubDate: Tue, 04 Jan 2022 14:12:43 +000

• Fabiano G. B. Brito; Jackeline Conrado et al. - Area minimizing unit
vector fields on antipodally punctured unit 2-sphere

• Abstract: We provide a lower value for the volume of a unit vector field tangent to an antipodally punctured Euclidean sphere ð•Š 2 depending on the length of an ellipse determined by the indexes of its singularities. We also exhibit minimizing vector fields v → k within each index class and show that they are the only ones that are sharp for the volume. These fields have areas given essentially by the length of ellipses depending just on the indexes in N and S.
PubDate: Tue, 04 Jan 2022 14:12:43 +000

• Bujar Xh. Fejzullahu - On the maximum value of a confluent hypergeometric
function

• Abstract: We study the maximum value of the confluent hypergeometric function with oscillatory conditions of parameters. As a consequence, we obtain new inequalities for the Gauss hypergeometric function.
PubDate: Tue, 04 Jan 2022 14:12:43 +000

• Vivette Girault; L. Ridgway Scott - Tanner Duality Between the

• Abstract: On démontre une relation asymptotique entre un modèle de fluides de grade deux et une classe de modèles de fluides non Newtoniens proposés par Oldroyd, comprenant les modèles de Maxwell de convection supérieure et convection inférieure. Ceci confirme une observation faite à l’origine par Tanner. On donne une interprétation nouvelle de l’instabilité en temps du modèle de fluides de grade deux lorsque ses coefficients sont négatifs. Notre approche inclut une démonstration simple de la convergence de la solution du modèle stationnaire de fluides de grade deux vers celle du modèle de Navier–Stokes quand α→0 (sous des hypothèses convenables) en dimension trois. Elle donne aussi une preuve de la convergence de la solution des modèles stationnaires de Oldroyd, quand ses paramètres tendent vers zéro, vers celle du modèle de Navier–Stokes.
PubDate: Thu, 25 Nov 2021 00:00:00 +000

• ( 1 + p q ) / 2 +and+ p q &rft.title=Comptes+Rendus+:+Mathematique&rft.issn=1631-073X&rft.date=2021&rft.volume=">Stéphane R. Louboutin - On the continued fraction expansions of
( 1 + p q ) / 2 and p q

• Abstract: The evenness and the values modulo 4 of the lengths of the periods of the continued fraction expansions of p and 2p for p≡3(mod4) a prime are known. Here we prove similar results for the continued fraction expansion of pq, where p,q≡3(mod4) are distinct primes.
PubDate: Thu, 25 Nov 2021 00:00:00 +000

• Haim Brezis; Alfred Bruckstein - A sharp relative isoperimetric inequality
for the square

• Abstract: We compute the exact value of the least “relative perimeter” of a shape S, with a given area, contained in a unit square; the relative perimeter of S being the length of the boundary of S that does not touch the border of the square.
PubDate: Thu, 25 Nov 2021 00:00:00 +000

• Olivier Pironneau - A Fast and Accurate Numerical Method for Radiative
Transfer in the Atmosphere

• Abstract: Pour résoudre les équations du transfert radiatif pour l’atmosphère nous nous tournons vers une formulation intégrale équivalente qui a l’avantage de ne pas contenir de fonction singulière. Une méthode itérative est proposée pour sa résolution et un résultat de convergence est donné.En corollaire un résultat d’existence et d’unicité est prouvé pour les équations du transfert radiatif, 1D en espace, sous des hypothèses assez générales sur les coefficients d’absorption et de scattering et leurs dépendances en fréquence.Une étude numérique termine cette étude ainsi que quelques commentaires sur l’effet des gaz à effet de serre sur la temperature de l’atmosphère.
PubDate: Thu, 25 Nov 2021 00:00:00 +000

• Olivier Lafitte - Unstable spectrum of a Rayleigh–Bénard system
with variable viscosity

• Abstract: This Note studies a Rayleigh–Bénard system in an infinite layer, in the case of temperature-dependent viscosity, with rigid boundary conditions for the velocity at the bottom and free-slip at a top of the layer. It states the linearized problem in the relevant functional operator set-up and identifies, for each nonzero transverse frequency k and Rayleigh number R the (finite) number of modes which are unstable in time. This number is equal to the number of eigenvalues of a particular operator which are smaller than R.
PubDate: Thu, 25 Nov 2021 00:00:00 +000

• Kanishka Perera - On the existence of ground state solutions to critical
growth problems nonresonant at zero

• Abstract: We prove the existence of ground state solutions to critical growth p-Laplacian and fractional p-Laplacian problems that are nonresonant at zero.
PubDate: Wed, 03 Nov 2021 00:00:00 +000

• Sergio A. Carrillo - A quick proof of the regularity of the flow of
analytic vector fields

• Abstract: We offer a new and elementary proof of the convergence of the Lie series giving the flow of an analytic vector field as well as a natural deduction of such series.
PubDate: Wed, 03 Nov 2021 00:00:00 +000

• Nguyen Bin - Some examples of algebraic surfaces with canonical map of
degree 20

• Abstract: In this note, we construct two minimal surfaces of general type with geometric genus p g =3, irregularity q=0, self-intersection of the canonical divisor K 2 =20,24 such that their canonical map is of degree 20. In one of these surfaces, the canonical linear system has a non-trivial fixed part. These surfaces, to our knowledge, are the first examples of minimal surfaces of general type with canonical map of degree 20.
PubDate: Wed, 03 Nov 2021 00:00:00 +000

• Alexandre Baldare; Rémi Côme et al. - Fredholm conditions for operators
invariant with respect to compact Lie group actions

• Abstract: Let G be a compact Lie group acting smoothly on a smooth, compact manifold M, let P∈ψ m (M;E 0 ,E 1 ) be a G–invariant, classical pseudodifferential operator acting between sections of two G-equivariant vector bundles E i →M, i=0,1, and let α be an irreducible representation of the group G. Then P induces a map π α (P):H s (M;E 0 ) α →H s-m (M;E 1 ) α between the α-isotypical components. We prove that the map π α (P) is Fredholm if, and only if, P is transversally α-elliptic, a condition defined in terms of the principal symbol of P and the action of G on the vector bundles E i .
PubDate: Wed, 03 Nov 2021 00:00:00 +000

• Duo Li - Projective bundles and blowing ups

• Abstract: Nous étudions l’éclatement X ˜ d’une variété projective lisse X le long d’un centre lisse B, munie d’une structure de fbré projectif. Si B est un point, X est un espace projectif. Si le nombre de Picard ρ(X) est 1, alors dimZ a une borne inférieure dimX-dimB-1. De plus, lorsque dimZ est dimX-dimB-1, X est un espace projectif et B est un sous-espace linéaire dans X. Si X est l’espace projectif ¶ n et B est une courbe, ou n est égale à 3 et B est une courbe cubique tordue, ou n est un entier arbitraire et B est une ligne droite dans ¶ n . Si X est une quadrique et B est une courbe, alors n est égale à 3 et B est une ligne droite dans Q 3 .
PubDate: Wed, 03 Nov 2021 00:00:00 +000

• Luca Berti; Vincent Chabannes et al. - Modelling and finite element
simulation of multi-sphere swimmers

• Abstract: Dans cet article nous proposons une méthode numérique pour la simulation aux éléments finis d’une classe de micro-nageurs. Ces nageurs sont composés par différents corps rigides qui peuvent bouger les uns par rapport aux autres. Nous appliquons notre méthode sur un exemple de micro-nageur connu sous le nom de Three-sphere swimmer.
PubDate: Wed, 03 Nov 2021 00:00:00 +000

• Stéphane Jaffard; Hamid Krim - Regularity properties of Haar Frames

• Abstract: We prove that pointwise and global Hölder regularity can be characterized using the coefficients on the Haar tight frame obtained by using a finite union of shifted Haar bases, despite the fact that the elements composing the frame are discontinuous.
PubDate: Wed, 03 Nov 2021 00:00:00 +000

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